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Chapter 1: Problem 45

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court's perimeter is 228 feet, what are the court's dimensions?

Short Answer

Expert verified
The dimensions of the tennis court are length 78 feet and width 36 feet.

Step by step solution

01

Interpret the problem and formulate equations

Let's denote the length of the court as \( L \) and the width as \( W \). From the problem, it is known that \( L = 2W + 6 \). Also, it's given that the perimeter \( P = 228 \) ft. Because the perimeter of a rectangle is given by \( P = 2L + 2W \), we can substitute \( L \) and \( P \) with their respective values. This will result in the equation: \( 228 = 2(2W + 6) + 2W \).
02

Simplify and solve for W

First, distribute the 2 in the formula which will give: \( 228 = 4W + 12 + 2W \). Then combine like terms to get the equation: \( 228 = 6W + 12 \). Then, subtract 12 from both sides which will be: \( 216 = 6W \). Lastly, to isolate the variable \( W \), divide both sides by 6 which gives the width \( W = 36 \) feet.
03

Substitute and solve for L

Since we know that \( L = 2W + 6 \), substituting \( W = 36 \) into the equation yields \( L = 2*36 + 6 = 78 \) feet. So, the length of the court is 78 feet.
04

State the final answer

So, the dimensions of the tennis court are length 78 feet and width 36 feet.

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