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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 pool are 40 feet wide and 120 feet long.

Step by step solution

01

Set up the equations

Let the width of the rectangle be \( x \) feet. Then according to the problem, the length of the rectangle is \( 3x \) feet. As the perimeter of the rectangle is 320 feet, create the equation from this information as \( P = 2L + 2W \) where L is Length, W is Width and P is Perimeter. Substituting the given values in, this equation becomes \( 320 = 2(3x) + 2(x) \)
02

Simplify the equation

Simplify the equation to form a solvable equation. First simplify the right-hand side of the equation: \( 320 = 6x + 2x \). This can be further simplified to: \( 320 = 8x \).
03

Solve the equation

Now it's possible to solve this equation for \( x \). To do this, divide both sides of the equation by 8. This gives \( x = 40 \). So, the width of the pool is 40 feet. And because we know the length is three times the width, the length of the pool is \( 3*40 = 120 \) feet.

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