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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 width (w) of the tennis court is 36 feet and the length (l) is 78 feet.

Step by step solution

01

Formulate the equations based on the problem

The perimeter of a rectangle is given by the formula \(P = 2l + 2w\) where \(P\) represents the perimeter, \(l\) the length, and \(w\) the width. The problem states that: 1) The length is 6 feet longer than twice the width. This can be written as \(l = 2w + 6\); 2) The perimeter of the court is 228 feet. This can be written as \(2l + 2w = 228\)
02

Substitute \(2w + 6\) for \(l\) in the perimeter equation

We substitute the equation for \(l\) from Step 1 into the perimeter equation, obtaining \(2(2w + 6) + 2w = 228\)
03

Solve the equation for \(w\)

Solve for \(w\) by simplifying the equation from Step 2: \(4w + 12 + 2w = 228\), which simplifies to \(6w + 12 = 228\). Subtracting 12 from both sides and then dividing by 6, we obtain \(w = 36\)
04

Substitute \(w\) into the length equation

Now that we have the width, \(w = 36\), we can substitute it into the equation for \(l\) that we developed in step 1 to find the length: \(l = 2(36) + 6 = 78\)

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