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Chapter 1: Problem 26

A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?

Short Answer

Expert verified
The dimensions of the pool are: width = 40 feet and length = 120 feet.

Step by step solution

01

Substitute known relation into perimeter formula

Since it's given that the length of the pool is three times its width, we can substitute \(l = 3w\) into the perimeter formula. The equation becomes \(P = 2(3w) + 2w = 320\), where \(P = 320\) feet is given in the problem.
02

Simplify the equation

The equation in step 1 simplifies to \(6w + 2w = 320\), which further simplifies to \(8w = 320\).
03

Solve for the width

To solve for \(w\), divide both sides of the equation by 8, which gives \(w = 320 / 8 = 40\). Thus, the width of the pool is 40 feet.
04

Calculate the length

As we now know \(w\), we can substitute it into the relation \(l = 3w\) to find the length of the pool. This gives \(l = 3 * 40 = 120\). So, length of the pool is 120 feet.

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