Problem

Art. The Mona Lisa was completed by Leonardo da V…

Problem 42 Easy Difficulty

Swimming Pools. The seawater Orthlieb Pool in Casablanca, Morocco, is the largest swimming pool in the world. With a perimeter of $1,110$ meters, this rectangular-shaped pool is 30 meters longer than 6 times its width. Find its dimensions.

Answer

Length $=480$ meters
Width $=75$ meters

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Video Transcript

Okay. Yeah. So we have a rectangular pool whose length length, which I'm going to? Right, L four is six m shorter than twice the width. Here's the with W. Okay, so the length of the pool is six m shorter than twice the whip. So that means that L is to w minus six. We also know that the perimeter, which I'm going to call p is 126 m. But what else do we know about the perimeter? The perimeter is twice the length plus twice with. So now we know that twice the length plus twice the width is 126. Okay, so what does that get us? We have L equals to w minus six and two. L plus two. W is 1 26. So we have a system of equations here. Okay. And we want to find the length and the width. Find the length. L. And the with W. So how do we do that? We have a system of equations here. So we need to solve the system. Okay now there's a couple of ways of solving a system of equations in this case we really want to use substitution or elimination but we already have one of the variables L by itself in terms of the other variable W. So in this case it makes more sense to use substitution. So I'm gonna take my other equation here and I'm gonna plug in what we have for L here in for L. And the other equation. Okay, so we have to and then instead of L I'm going to write to W minus six plus two W. Is 1 26. Okay, so now we have an equation with just W. So let's solve for W distribute the two and we have four W minus 12 plus two. W is 1 26 at 12 to both sides. And combine these like terms four W. +12 W. So we have six W. Is 1 38 divide by six. Ws 23. Okay we have W. Now and we need L. The length so we can go back and go to either of these equations and plug in what we have for W to get L. Now we already have L by itself in this first equation and that's what we want to solve for. So let's use the first equation. Okay, so let's let me copy this. Okay so we have L equals two. W. My six W goes 23. So let's plug in what we have for W. L equals two times 23 minus six, which is 46 minus six and that's equal to 40. Okay? We have L equals 40. The length is 40 the width is 23. Yeah.

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