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Chapter 1: Problem 46

The length of a rectangular pool is 6 meters less than twice the width. If the pool's perimeter is 126 meters, what are its dimensions?

Short Answer

Expert verified
The width of the pool is 23 meters and the length is 40 meters.

Step by step solution

01

Formulate Equations

Let's denote the width of the pool as \(x\) meters. Since it is given that the length is 6 meters less than twice the width, we can express length as \(2x - 6\) meters. The formula for the perimeter of a rectangle is \(2 * (length + width)\). We are given that the perimeter is 126 meters, so we can substitute the expressions for length and width into the perimeter formula to get: \(2 * (2x - 6 + x) = 126\).
02

Simplify The Equation

Before solve the equation it will be helpful to simplify it. The equation from the previous step we have such as after multiplication \(6x - 12 = 126\). Now we can add 12 to each side of the equation to get \(6x = 138\).
03

Solve For x

To solve for \(x\), we need to isolate \(x\) on one side of the equation. We achieve this by dividing each side of the equation by 6. So, we have \(x = \frac{138}{6} = 23\).
04

Find The Length

Now we can use the value of the width (\(x = 23\)) determine the length. Substituting \(23\) into \(2x - 6\), we get \(2 * 23 - 6 = 46 - 6 = 40\) meters.

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