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Chapter 0: 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 rectangular swimming pool are a width of 40 feet and a length of 120 feet.

Step by step solution

01

Understand the Problem

The problem gives that the rectangle's length is three times its width. And the perimeter of the rectangle (the pool) is 320 feet. The formula for the perimeter of a rectangle is \( P = 2l + 2w \), where \( l \) is the length and \( w \) is the width. Substituting the given values, we have the equation: \( 320 = 2(3w) + 2w \).
02

Simplify the Equation

We can simplify the equation by multiplying to get: \( 320 = 6w + 2w \). Combining similar terms leads to: \( 320 = 8w \).
03

Solve for w

To find the width (\( w \)), divide both sides of the equation by 8. So, \( w = 320 / 8 = 40 \) feet.
04

Determine the Length

Now we know that the width is 40 feet. Since the length is three times the width, the length, \( l = 3w = 3 * 40 = 120 \) feet.

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