Problem 45 - College Algebra

Question

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?

Step-by-Step Solution

Answer

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

Step 1: 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: \( 228 = 2(2W + 6) + 2W \).

Step 2: 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.

Step 3: 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.

Step 4: State the final answer

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