Problem 43 - 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 width of the tennis court is 36 feet and the length is 78 feet.

Step 1: 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.

Step 2: 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 \(228 = 2L + 2W\).

Step 3: 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 \(228 = 2(2W + 6) + 2W\).

Step 4: 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 \(W = 36\).

Step 5: 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 \(L = 2*36 + 6 = 78\).