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Chapter 1: Problem 43

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 of the tennis court is 36 feet and the length is 78 feet.

Step by step solution

01

Express the length in terms of the width

From the problem, it's stated that the length of the tennis court is 6 feet longer than twice the width, which can be formulated as \(L = 2W + 6\). Now, you have linked the length L to the width W.
02

Write down the equation for the perimeter

Knowing that the perimeter of a rectangle is the sum of twice the length and twice the width, we can set up the following equation: \(P = 2L + 2W\). Since it's stated in the problem that the perimeter is 228 feet, we can substitute P with 228, getting \(228 = 2L + 2W\).
03

Substitute the equation for L into the equation for P

Taking the equation for length which is \(L = 2W + 6\) and substituing it into the equation for P, that is in place of L. Therefore the equations becomes \(228 = 2(2W + 6) + 2W\).
04

Solve the equation

To solve the equation, first simplify it. \(228 = 4W + 12 + 2W\) which can be expressed as \(228 = 6W + 12\). By rearranging the equation to solve for W, it results in \(216 = 6W\). Finally, by dividing each side of the equation by 6, we have \(W = 36\).
05

Find the length

Having calculated the value of the width to be 36 feet, it can be substituted into the length formula obtained from the problem: \(L = 2W + 6\), and replacing W with 36, gives \(L = 2*36 + 6 = 78\).

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