Problem 27 - Algebra and Trigonometry

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 36 feet in width and 78 feet in length.

Step 1: Define the Variables

Let’s define the width of the rectangle as \(x\) feet, and because the length is 6 feet longer than twice the width, define the length as \(2x + 6\) feet.

Step 2: Write Out the Perimeter Formula

In this case, a rectangular perimeter equals twice the sum of the length and the width: \(P = 2*(l + w)\). Substituting the specified parameter \(P = 228\) feet: \(228 = 2*(2x + 6 + x)\).

Step 3: Solve the equation

Solve for \(x\) using algebra: Simplify the equation to \(228 = 2*(3x + 6)\), which will give \(114 = 3x + 6\). Further simplifying, subtract 6 from both sides to get \(108 = 3x\), then divide both sides by 3 which will yield \(x = 36\). This value corresponds to the width. Substitute \(x = 36\) into \(2x + 6\) to find the length, which equals \(78\) feet.