Problem 45 - College Algebra Essentials

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

Step 1: 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 \(2l + 2w = 228\)

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

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

Step 3: 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 \(w = 36\)

Step 4: 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: \(l = 2(36) + 6 = 78\)