Problem 44 - College Algebra Essentials

Question

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?

Step-by-Step Solution

Answer

The dimensions of the swimming pool are 40 feet wide and 120 feet long.

Step 1: 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 \( 2(3x) + 2x = 320 \).

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.

Step 3: 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.