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Pre-Algebra - 5.1 Perimeter and Area

Added Jan 27, 2021 •

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Setup and Solve Variable Equations relating to: The Perimeter of Triangles and Rectangles The Area of Triangles and Rectangles Know how to Identify the Height of a Triangle Be able to solve/isolate any variable in a formula using Inverse Operations

Show Transcript

hey perimeter and area let's go do a quick thing Eric so 51 perimeter and area in professional baseball the infield diamond is actually a square yeah we call it Diamond because it's not going to go flat but if you had turn it around like that the baseball diamond is actually a square it's just a regular diamonds so is actually a square that measures 90 feet on each side if s represents the length of the side of the square than 4S would represent the distance around the square distance around that's perimeter but let's go through this right here quickly run through a mental math so that's we're going to do if each side is 90 90 90 90 90 4 times each side is 94 * 90 is 360 ft but let's do a quick thing right there so let's go for S4s perimeter Square notice I wrote perimeter of square not this perimeter cuz the perimeter is an ever-changing thing depending on your shape is your polygon and it's called the circumference for a circle that anything was angles is called the perimeter anyways 4S and they tell you the S equals 94 time 90 equals 360 ft that is the perimeter that's the perimeter the area though I'm jumping ahead just to show you the difference area of a where is the side squared s squared in this case it's 90 8100 look at the difference let's assume outside so all right so we can the perimeter is 360 feet where the area is 8100 square feet how are you guys knew the foreman but you don't know the difference and why why is perimeter so much so much bigger cuz they're different types of measurements all right you guys are doing the work without understanding sure I had I should just lock this them up anyways so perimeter so you got this diamond this baseball diamond that should be a diamond should be a perfect score but it's not but let's assume it is 90 90 90 is this was a paperclip and you unfolded it right here what a perimeter is the actual straighten length so it's just one link you with a shape of something and unfocused just think about offense if this was a fence around a square lot and you unfolded this Square you would start at zero this would be 90 should be 180 this is b270 and 360 so if you unfolded this and made a straight line just imagine a paper clip that you straightened out you would have a length that's the total length so 360 ft but let's make this a square where the eye idea of area comes from area is the space inside how do you measure a space inside so instead of instead of and saying that this is 90 ft imagine you have 90 Rose that are 1 foot wide so here 1 2 3 yeah it's super small I'm sorry and so you get to the bottom row which is 90 and they're all equal 1 2 3 at each one of these is one unit or 1 foot wide at the same time you have 90 going this way but instead of seeing it as 90 feet across columns and look what happens when I make 90 columns I make little squares when they crisscross each other they end up being squares until I get to this right here this is my last one and look at it this way can a multiplication chart 90 x 90 each one of this I got three rows here in two columns three times you can literally see I got six squares 6 square units and if I got 90 of them this last one right here that's a D100 8100 little squares and that's what square feet is each one of these represents a one by one 1 foot by 1 foot that's what's called a square unit so we got 8180 square units that can fit inside so area is about always finding a little square not just a little square how many little squares fit in well as perimeter you just going around turn around and just imagine taking it apart and flattening out you got a lynx so now let's go this right here perimeters of formula so look for S that's just another way of saying s + S + S + S why is it fluoresces because A square has the same length on all four sides and you just four four sides at you look at a perimeter of a this right here quick picture the perimeter of a rectangle there's a rectangle what's the length width and length but then there is the width and length in a triangle decides to be the same but we don't know what we're going to assume they're all three different size a b and c so the perimeter is the perimeter is the sum of all length of the size but some shapes because of the way they are have a special formula like a square all sides of the same 4S butt length + width or length length + width + length hey so we have two lengths why don't I just double it to Lynx Plus 2 wits or hey why don't I just add my length and width and double that instead of doubling separately noticed we got three set formulas for perimeter of a rectangle with all the sides individually or we could double the length double the width and add those two numbers together or I can just add my length and width and double the perimeter of a rectangle the sum of twice the length and twice the width triangle we don't know what the sides are three sides that's why it's just adding all the sides up so you got to know the difference so just going over now from now on you need to write a variable statement a variable equation don't just go straight and give all the numbers p A + B + C the perimeter of this triangle is side A PSI B plus size see which one's a b and c that's what you got to realize the choice is yours so that's how we're starting with some simple Concepts there's a lot of times when guys get to algebra guess what what's what you guys freaked out it doesn't matter cuz we're going to add them all a b and c so 12.8 + 17 + 28 5 notice I went this way this decide to go that way it doesn't matter I'm at it all three of these up you get 58.3 so try this first one out on your own and I'll do it in 7/32 find the perimeter of a rectangle with length 15.2 and with 10.5 slightly different find the perimeter of a what time with Mike 15.2 and with 10.5 that mess you going to show it three different ways try it on your own take 30 seconds out of your time & life from watching and playing games cuz I see you guys know that if you guys are on something there's glare there's a reflection for playing a game or watching a show the lights that flash they change in front of your face the Shadows I can see that that's why it's smart to be in a well-lit room cuz they're less Shadows so right here find the perimeter of a rectangle with length of 15.2 and width 10.5 every know which way is better the choice is yours so let me draw a diagram of the rectangle first 50.2 simple Tire thank you everybody thank you for putting in your answer and letting me know you did it now this right here is my picture a diagram the other side's how come I didn't label the other sides does my diagram how come I did not label the other sides got to watch out for that last number right there how can I label size right here and here equivalent to what I'm glad you said that so got to watch out so math so I need I need a lot of guys to start so almost almost we're going to treat this like English class so the you three people gave me pretty much the same thing because it's the same as the other size it it's already there that right there in English if this was an essay you get a c for your essay I know what you're saying but notice I put notes on your Sosa what do you mean why because it's already so like I said equal to the other side what other side so that's why you we need you guys to start thinking about math and English connected think about the thought process that about making things clear I totally understand what all of you guys typed in but if this was an essay but it's not an essay would be like this in a rectangle opposite sides are equal the word would be congruent but you'll get there so you know the saying the length and the width are the same I get what you're trying to say but if this was an essay it's all in the detail so why do you guys are going to be getting into in was 6 years from now you'll be starting College and their urine to be happy going to be put in a situation to figure out what you want to focus on and a lot of guys are going to be in a detail-oriented thing some because you'll be biologists chemists you know you're going to have to write detailed reports and it can't be generalized so that's what the specific thing you guys need to do so opposite sides of a rectangle are congruent opposite sides of a rectangle are equal so I don't need to label that but that's what makes this hard a lot of you guys follows my and you did this and that was a there's a perimeter no perimeter is going all the way around and this is a common geometry thing that they're going to do the same thing on the on the Run start a lot of guys missed a question on this cuz it label the picture the same way you chose this as your perimeter and you lost points thank you for not paying attention those are you guys this is the same people that miss this question this was an easy question but they decided to tricky with the picture what's the perimeter all you need to know you add the side but you only saw these two listed in your mind you needed to understand that yes the opposite sides of a rectangle are the same we are visual your visual learners if you do you guys didn't see that you didn't add these to that's where you guys just left that as this so depending on which formula you decided to choose perimeter is length + width + less with if you decide how to put this in the drawing or understand that smartest thing in math is always to write down a formula when you write down a formula you have something to substitute into you will never mess up in the basics when you write down a formula but which one do you choose and imma show you it's the same thing choice is yours what do I have 10.5 length is 15.2 + 10.5 + 15.2 + 10.5 and then you'd added together you would get what is this 51.4 and this right here you would double your leg is to Point 2 + 2 * 10 point if I double that that's 30.4 and I double that that is 10 that's 11 3 + 10 4040 + 141 that's double that's not 11 double would be 21 30 + 20 + 50 + 1 + 5151.4 that seemed pretty simple and this one right here I go to x length and width 15.2 + 10.5 this right here get you 25.7 right double 25.7 a double 25 is 50 double points 7 is 1.4 they're both similar in thinking but this one I think is a little bit easier and mentors a mental math but this is the same but this right here would have to add one of them than one than one that's why you guys learn algebra to stop was called the redundancy and I was real where they're going to get going to work backwards what if we give it to the printer you're at the find the missing units so let's look at example to all right the perimeter so right here let's write down the statement something I downloaded it but pretend you didn't let's go work on this together so the perimeter a rectangle is 42 ft if the width is 10 feet what is the length resume out sorry thank you so this is pretty what you're going to be doing you're going to be asked to solve this stuff right here the perimeter of a rectangle is 42 ft if the width is 10 ft what is the length and this is as bait we start with this we're doing these multi-variable things or or multi stop things and we're doing geometry basic Jam this basic super basic geometry the why we have this because one of the ideas that we always say to you guys is always show your work but especially in work is a picture if you actually write and draw a picture a sketch it always helps you sort through your logic so let's do this quickly so what's not here is a diagram of a rectangle I know that my perimeter equals 42 my width is 10 I could put 10 right here I don't know what this is let's put the letter L you can put X if you want but I must do and there it is I have enough information to set up something why do you guys would say this is why if you guys only that why you guys were just go if you guys many of you that didn't have a diagram cuz this was the question on the ren star if you guys got to this we know the perimeter is 42 the perimeter rectangle and it's up to you to decide what you want to set it up as and here's the thing if you wrote down the formula it would be nice here's where some people messed up the errors checking the errors on 42 is your perimeter we don't know what the length is so you go to l and a lot of guys put this right down here 42 equals 2L + 10 + that's where you're messed up it's a simple, mistake but you forgot that you're adding two times the width and this just represents 1 width so you actually need to do that right there it's not 10 it's 2 L + 20 so becomes a two step equation 42 equals 2 plus 20 not 10 that was the common mistake a lot of guys made and so what are we doing with perimeter with algebra you're just setting it up to understand how to write an equation that's why we're doing something using something you guys know to build up so right here what are we do we done subtract 20 on both sides track 20 I only make sure the work is equal on both sides that's correct 20 - 20 is a zero we're left with this to our let's bring that down too well equals 42 - 20 what is that 22 divided by 2 your length is 11 length is 11 so equals 11 equals 11 algebraic way which is fine but it doesn't write an equation you guys have to understand how to set up an equation to the equation was this right here that's the main thing how to set up a two step equation I just did this 42 -10 equals 32 and then you wrote -10 equals no it doesn't understand what you're doing you're just going you're being lazy 42 - 10 is 32 but 30 - 10 does not equal 32 minutes and could you keep on doing your work till you get your answer 32 - 10 22 and then you know you got those two sides divided by 2 is 11 but this is incorrect syntax meaning you wrote sentences that don't make sense if this was English class again 42 - 10 doesn't equal 32 - 10 I know you're just continuing your work but these are not equal these two end up being equal at the steps in the middle don't so you have what's pretty much and incorrect explanation yes totally works too cuz that you're using the other formula so let's write down the other formula and you'll get the same answer perimeter equals two times length plus width we don't have the link two times the length that's 42 it's right that 42 equals two times length we don't know where this is what again in 10 that's a ten and then we got double this alright let's get rid of it and instead of Distributing there's two ways you can do this problem instead of Distributing the too cuz it be distributed to you end up with this get back to her but let's / 2 first divide both sides by 222 equals L + 10 let's subtract 10 it's too well what did I do man that's 21 thank you half of 42 is 21 subtract 1021 - 1011 equals L same thing but you got to start with the formula first start with some equation that you plug things in and work backwards it's up to you which one that's the thing 2 L + 2 W or two times choice is yours set up the next one the question is this the perimeter of a rectangle is 26 yards it's length is 8 yards find the width set it up so you can figure which one you're doing on your own I slept yes we are almost done good job type in the number when you got your answer the perimeter of a rectangle is 26 yards it's length is 8 find the wit the whole thing is knowing how to write an equation not just do the work while you guys are stuck this doing step by step by step by step until you get to the answer alright alright alright so I got a couple different answers but the thing is for LA to you is what do you set up with for you somebody said so messed up I got a couple different answers and said do I do a picture first or do I do an equation first in Geometry I would always suggest doing a picture first but let's ignore this as a geometry problem and let's just see it as an show me the formula good good keep typing it in to let me know that you got it but let's start with the front we know it's a rectangle we know the perimeter is 26 so I'm going to start perimeter equals 2 W + 2 L doesn't matter which one comes first choice is yours it's all the same so we know the perimeter is 42 I don't have the width but I do have the length the length is 8 yards and that's why having a formula or some type of an idea to start with is pretty important it keeps you in check notice how I line things up think about the formula as your topic sentence and then when you have a topic sentence you always got to do your introductory paragraph it's not just so feeling so I'm telling my perimeter equals to Douglas too well well I know what the perimeter is so let me plug it in my perimeter is 42 I don't have my with but I have my length it creates a roadmap for you to follow an equation of formula lines things up keeps you organized so let's go through this 42 doesn't change to W doesn't change but I could clean this 2 * 8 to make 16 then we subtract 16 on both sides and then I got my equals I notice how I try to keep my equal sides lineup even as ugly as a man writing is it's not perfectly straight but it's straight enough organized forget knowing adding subtracting multiplying dividing those are common mistakes the next next space worm people make mistakes and staying organized as ugly as my handwriting is I always try to keep things lined up so at least I can follow my work so 2W doesn't change to bring this down to 16 - 2 when is a zero that got zeroed out 42 - 16 what is 42 months 312 36 and then oh thank you thank you thank you thank you I was looking at the old problem the air is a perimeter is 20 6 so let's grow well that out but the work on this sides correct thank you the perimeter is 26 good touch one person you shouldn't be a vet you should be an animal catcher hunt them down Butterbean the vet just BBB animal catcher get to hunt them down you hunted down the right thing and the detail 26 - 6 that becomes 20 20 / 2 we could be both sure animal catcher and abet West / 2 / 2 which is 10 set right let's check it out perimeter is 26 right now what did I mess up on see when I mess up perimeter is 26 yards to width and double double 6th so it's 16 that's another catch thank you so that becomes and 10 divided by 2 is 5 thank you the whole thing once you start with one mistake yes thank you 16 so let's double-check her work so the length is 8 length is 8 perimeter 8 + 8 is 16 S5 IMC I messed up again 5 + 5 is 10 16 and 1026r perimeters to 6 checking her answer so yeah so when you mess up your mess up but catching up catching on. It is but so area of a rectangle no one ever really forgets cuz we learn it area is length times width of a rectangle show me guys learn the gave me the formula for the area of a trapezoid send you guys gave me the air for you guys know all that stuff but we're only doing rectangle triangle Winton Woods that is for length and width is what we use for pretty much before geometry after geometry length and width becomes Bay and height so I don't want to write on this cuz I want to but the base is pretty much the bottom or the top of a rectangle bottom or top the height is how tall it is so length and width are also known as Basin height that's where this changes in but most people don't understand why the area of a triangle is 1/2 the base and the height I'm going to do it two different ways to show you so let's say we have a rectangle instead of calling it lengths and widths let's call it base and height where does the area of a triangle come from because right here if we cut a rectangle into two equal triangles this is also the height so the area of the whole thing is just base times height as a rectangle area of a rectangle is base times height but when we cut we just called the diagonal we go from corner to corner and cut into two equal we only look at one triangle that would be half the rectangle the area of a triangle is half the area of a rectangle and there's two ways to do it base times height over 2 or 1/2 base times height it's up to you decide what you want to do first you want to know what's the same thing you multiply base times height and then / 200 you multiply base times height and then you take half of it saying it differently but you still you know there's another way looking at this so let's use a triangle they give us and this is called and they always use what's called an equilateral triangle so these two sides are equal and so this is the height right here your height is how tall something is so that's your age and your base is pretty much the bottom sometimes or triangles drawn the other way she's on top so basis top or bottom so here's our base here's our height why is it 1/2 base times height look at this right here from here Tahir this whole Wing is my base if this height should cut the bottom side in half so this right here is equal to this right here so is this my base that means the length from here to here is one half my base and imagine this right here I'm going to use my now I'm use blue I dropped my blue something is my green then let's say I took the stronger I hear these two triangles are equal what if I put this triangle in swivel that over this like a swivel point I'm taking this and I'm going to drop it down wouldn't this just flip over and make and complete a rectangle the height is the same that's H what is the length from here to here 1/2 my base and I just made a rectangle what's the area of a rectangle length times width what's my length 1/2 my base what's my Sir with whatever the other one is H 1/2 x h 1/2 BH area of this triangle is 1/2 base in the area of this rectangle is 1/2 base times height but this rectangle for my knee just flipping that other piece over so these are two ways to describe where the formula for a triangle came from that's why it's 1/2 base times height height do X you don't know what the height is the height is how tall something is so and it needs to be stopped for a second just imagine when you were younger and you're you're you're you're my One Direction cared about you cuz I don't care about you anymore anymore when you work you to them and they measure height they put you against the door jamb and they put marks on the door and what did they say to you stand up straight so they can measure you that's what I like straight and a height is always formed buy right angle what you don't see here why is this side the H because that's where the bass goes purple regular straight up and thinking right here your height is where the right angle is on a triangle all right always form the right angle so let's look at this first one and then we'll do a guided practice base of a triangle is 12 in and the height is 5 and 1/4 inches find the area so you don't even need a picture they gave us the words the base let's draw this out the base of a triangle is 12 in the height is 5 and 1 quarters do not change it to a decimal deal with it as a fraction they literally told you what you have you don't need a picture if they tell you what you have as long as you have a formula area equals 1/2 base times height and 1/2 what's our base 12 what's your height 5 and 1/4 all right and what's great about this you could you don't have to say you do not have to multiply base times height first what's half of 12 that is 6 what is x 5 1/4 mixed numbers change it to an improper fraction 2021 over 4 but again multiplying fractions 6/1 * 21/4 let's simplify this let's / 2 + / 2 that would get me 3 and then I would have 3 * 21 what is that 63 63 / 2 half of 63 while we don't want to go to 62 62 is 3131 and 1/2 31 1/2 or 31.5 so look at that right there that's simple try this your own and they're making it easier for you because there chose not to do a triangle the width of a rectangle is 11.4 M and the length 18.9 m find the area take a second out put it in once you have that the width of a rectangle is 11.4 and it's length is 18.9 find the area and once you're done take you 45 seconds at most and you don't even need a lot of space to do this ? three of you guys did that never never never do that never ever put a? With your answer it's like baby will be confident even if it's there's a thing in real life it's the if you're not sure and someone ask you for something and it's one of those test questions like an interview don't say even if you're not your grandpa's right you answering or no you know and if you're wrong be able to accept it and be willing to accept practice alright alright alright I was supposed to. So we know the area of a what is length times width and they set it up nicely are we're looking for the area the length is what what is the length the length is 18.9 and the width is 11.4 and always do is multiply 18.9 11.436 carry a 330 235 carry a 3/4 in that seven is there a placeholder 18920 placeholder 189 and then we added together 614 carrier one what is that one nine 10 10 and 15 is 25 carry a tune that's 11 carrier one 215.46 square feet I am never going to not watch out the  watch out that right. I understand where you did the estimation but you got to multiply and make sure you add right line up your decimals and what not lie your decimals and then multiply more we got you guys some places I'm never going to force you guys in this class right now but you should get in the habit of right the units out when you guys get further and further if you getting a bad habit like me and keep on forgetting the regular units out it's going to hurt you down the line cuz you always stop when you get to a point of specially in chemistry some of you guys are going to be nice I think you'd be excellent being a class with Juniors and seniors yeah and you can do that or to square meters even I missed the thank you but put the square it should be meters square meters thank you sometimes your units don't match up and that's when you mess up you got to make sure the units are the same and convert them to the same units so Square all that and remember you guys are good multiple-choice what if there's 2 oz of 215.461 is square meters one is just meters the one without the square is the wrong answer so watch for those little things all these little details they're going to trick you guys and make sure that you do not go to the College of your choice because you are not a detail-oriented person and you end up being like me be better than me don't miss out on the details I want you guys to become super successful so I can free load off of you when I retire cuz you're going to be super rich and then I'm going to end up working a nice and I'll be part of your entourage you're going to pay me ton of money partner Entre thank you I will take that job alright let's give this a word problems right here listen to this Tyler has enough blue paint to cover 800 square inches he wants to paint a rectangular stray on his bedroom wall that is 120 inches long find the width of the section he can paint so we know we're going to do something so Tyler has enough to paint and cover 800 square inches so they give you the area and they give you how long it is we just got to figure out how wide it is alright so word problems we know it's going to be a rectangle so area equals length times width and I took this away for reasons so you don't look at the steps positive paint to cover 800 square in that tells us that the area and we know how long that stripe is going to be because the length is going to be a hundred twenty in long and the units are so it matches up 120 W and it's that simple right there there's your algebraic equation we have started out with the formula and then we plugged in what we knew we have one another and this is typical in algebra why do people freak out I got two different three different and substitute in in Algebra 1 usually you're eliminated bring it down oh we don't we eliminate all these other variables when we substituted and we end it with one variable once you have a one variable since situation we know what to solve for so and it's that easy let's / 120 I'm going to show you I solved it differently than the book so 120 / 120 that is 1w which is just another way of writing W I wrote that extra bit down just to show you that's a one not a zero and then let's simplify this right here 0 / 0 we can simplify that we had 80 well we can divide by 4 if I divided by 4 and up with 20 / 4 / 3:20 / 3 that is a writing 6 2/3 volume at 6 2/3 but let's look at this right here all I did was substitute in I'm going to what they did and why cuz a lot of guys going to be wondering why does it look different so what are we looking for we're looking for the wits we're looking for the wit look what they decided to do they wrote down the area formula first air equals length times width but they decide were solving for w well why don't I just make it double You by itself first then I plug it in spelling of this I want W what's keeping W from being by itself the length is length times width I want the width so what they decide to do is divide both for the length length Rover length one leaving you with w and then you have this brand new formula the width is the area divided by the length and they decide to plug it in area is 808-2120 we got the same answer this right here is called solving the solving for the variable sometime this is actually one of the harder questions a lot of people get in the very beginning in the future you guys are going to actually be able to do this another example and a second of this let's do this one first Flags the area of a triangular flag case shown is 69 Square in find the height of the case notice they gave you information find the height of the case gave you the information in the diagram let me zoom in the area of the Triangular flag case shown is 69 SQ find the height of the case and this right here it's not in the words sometimes word problems utilize the picture not all information is in the word do this on your own the answer up when you are done quite remember we're looking for the area that's why this stuff is very important know what you're looking for looking for the area of a triangle write down the area so that it's only got your stuff the area formula for a triangle first and substitute in and work backwards right down the area formula and we're totally that's good that's very good right there so what's the Heights different things but let's go work through this all right since most you guys are so let's look at this they gave us the area the area of a triangle is 69 square inches and this right here represents the base 23 siletz plug-in in the equation right here before I do anything let me write down the formula this one little step is where some of you guys don't do and you just go straight and that's where you at you get lost startup organized area of a triangles area equals 1/2 base times height and how about I plug things in the area is 69 square feet 1/2 my base was in the picture which was 23 * the heights there's a lot of things you can do 1/2 * 23 I'm going to do a couple things right here let's get rid of 1/2 1/2 freaks out a lot of cuz then you have a decimal I don't want to do it to decimal what's half of 23 so I keep things balanced this is what makes algebra algebra sometimes you can go back a lot of people think I got a x in math as long as you keep things equal whatever you want even if it's wrong cuz you could always correct it as long as things are done correctly when I say correctly equivalent you can do whatever you want I'm going to multiply both sides by 2 2 * 69 to x 1/2 23 + H2 x 1/2 that makes one 2 * 9 but you got right there is 138 right yes 138 equals 23 H and let's / 23 and then what for that is that's your height what is a 3 times what gets me something with an 8 at the end 3 * 6 gets u18 so let's check that out 3 * 6 can you carry a 1/6 * 2 is 12 1238 your height is space let's do it another way so why do you guys got two here and got stuck and got me lot of different numbers let's do the decimal way there I'm going to do the same thing 69 equals 1/2 * 23 * H let's do the 1/2 * 23 first then 69 equals 1/2 of 23 - 22 is a lot that's what is 11 + 1/2 what's 7 as a fraction 23 over to H now let's let's let's get rich Bliss 23 and 1/2 I want H so let's multiply by the reciprocal 2/23 * 2 over 23 hey look at this 2-ton to 6900 create where did I ain't going home the reciprocal 23 + I / 23 look at that hundred thirty-eight over 23 same thing which one's better choice is yours your whole goal is to know how to do inverse operations how do you get rid of this what's the inverse what's the what's the opposite how do you get the herbal by itself now let's do it the way the book would have liked you to do it how do you we're looking for the height and we'll plug it in after area equals 1/2 base times height all right let's go I just want height to be alone how do I just get it equal to H so I can plug in to this side and just have H let's first get rid this one have multiply both sides by the reciprocal 2/1 * 2 / 1/2 / 1 * 1 / 2 that's a one that leaves me with base times height and then now I have 2 * my area I just want the height Soylent / my base what's my base right here so now I have base over bases one leaving me with height to tie the area / the base what was the area 2 * 69 what is the base 23 in same thing so what they want what they want you to understand is know how to if you have a formula know how to get a variable by itself and that's actually a couple your problems in your homework your class or if it's just one two and three but before we move on I'm going to make something up this is a typical formula equation solve for and I'm going to make up some of them to stay soft for G so here's a softer G when it says solve for a variable Indians get the variable by itself and this is on the homework this is how do you get this variable by itself we're not going to find exactly what the number is but you're going to have to make a new formula so the formula for this is k equals m - 3 G what is g o g is not a number in this case cuz we don't have M&K but you can get this by itself so the whole thing is what do you do first the coefficient is always a lot always coefficient usually is the last thing you get by yourself so get rid of what's not a coefficient get rid of that subtract m we subtract m m - + 0 but K and M are not like terms so we need to just rewrite that as an expression K - M equals -3 G and this right here test a lotta guys messed up on you forgot to bring down the negative the negative the -3 is a -3 and it goes with the three so you got to bring that down to positive signs of the only things you do not need to bring negative this is -3 * G you need to see this is -3 * G so you can do the inverse operation is divided by -3 so -3 divided by -3 that's a positive one you're left with just G and what is g equal to K - M / -3 that is solving a formula when you have multiple variables maybe some coefficients and constants how do you get the variable by itself so this is couple The Challenge questions you're solving a formula what it means is whatever letter you have right here you're getting this by itself M if it said solve for M man that would have been super simple solve for M if if I said solve for M using the same same same equation ke equals and -3 G is my Adam what's keeping him from being by yourself 3-g Wireless at the Regina besides if we end up with k + 3-g equals solving for the variable if you don't have the other values for the other variables it just means how do you use your inverse operations to get this variable bicep at the end so those are a couple of Challenge questions

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