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Chapter 1: Problem 44

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 a width of 50 yards and a length of 100 yards.

Step by step solution

01

Set up the Equation

Denote the width of the field as \( x \) and the length as \( 2x \), since it is twice as long as it is wide. The perimeter of a rectangle is given by \( P = 2l + 2w \), where \( l \) is length, \( w \) is width, and \( P \) is the perimeter. Therefore, the equation from the problem statement is \( 300 = 2(2x) + 2(x) \).
02

Simplify the Equation

Simplify the equation to make it easier to solve for the variable. \( 300 = 4x + 2x \). Merging like terms will give: \( 300 = 6x \).
03

Solve for \( x \)

Now that we have a simple equation, we can solve for \( x \). Divide both sides by 6 to get \( x \). We get \( x = 50 \). Therefore, the width ( \( x \) ) of the soccer field is 50 yards.
04

Solve for \( 2x \)

Next we need to find the length of the soccer field. Using the relation \( 2x = l \) , substitute the value of \( x \) that was calculated in the previous step. We get, \( 2x = 2(50) = 100 \). Therefore, the length of the soccer field is 100 yards.

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Most popular questions from this chapter

In Exercises \(69-72,\) use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$ (x-2)^{2} \leq 0 $$

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