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Chapter 0: Problem 25

A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?

Short Answer

Expert verified
The dimensions of the soccer field are 50 yards wide and 100 yards long.

Step by step solution

01

Understand the problem

A rectangle's perimeter is the sum of all its sides. In this case, this is 300 yards. The length of this particular rectangle is twice its width. These are the main clues needed to set up and solve the equation.
02

Set up the equation

Designate the unknown width as \(x\), then the length will be \(2x\). Therefore, the formula for the perimeter becomes \(2(x + 2x) = 300\).
03

Solve the equation

Simplify the equation first to \(6x = 300\). To find x, divide both sides by 6, this yields \(x = 50\). Therefore, the width of the field is 50 yards.
04

Find the length

Since the length is twice the width, calculate it as \(2 * 50 = 100\). Therefore, the length of the field is 100 yards.

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