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Chapter 1: Problem 44

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 swimming pool are 40 feet wide and 120 feet long.

Step by step solution

01

Understand the problem and translate it into an equation

We are told that the pool is a rectangle. The perimeter of a rectangle is determined by the formula \( P = 2L + 2W \), where \( L \) is the length and \( W \) is the width. Now, we know that the pool is three times as long as it is wide. So, if we let the width be \( x \) feet, then the length is \( 3x \) feet. We also know that the perimeter is 320 feet. So, we can write the equation as follows: \( 2L + 2W = P \) becomes \( 2(3x) + 2x = 320 \).
02

Step 2:Solve the equation

Solving the equation \( 2(3x) + 2x = 320 \) simplifies to \( 6x + 2x = 320 \), which then simplifies to \( 8x = 320 \). Solving this equation for \( x \), we get \( x = 320 / 8 = 40 \) feet.
03

Determine the measure of the length

Since the pool is three times as long as it is wide, we can find the length by tripling the value of \( x \). So, \( 3x = 3 * 40 = 120 \) feet. So, the pool is 40 feet wide and 120 feet long.

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