Question

1. the perimeter of the tennis court is 228 feet. what are the dimensions of the court? image of a rectangle with width labeled w and length labeled 2w + 6

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Here, the width is \( w \) and the length is \( 2w + 6 \), and the perimeter \( P = 228 \) feet. So we substitute into the formula:
\( 228 = 2\times((2w + 6) + w) \)

Step2: Simplify the equation

First, simplify the expression inside the parentheses: \( (2w + 6) + w = 3w + 6 \). Then the equation becomes:
\( 228 = 2\times(3w + 6) \)
Divide both sides by 2:
\( \frac{228}{2} = 3w + 6 \)
\( 114 = 3w + 6 \)

Step3: Solve for \( w \)

Subtract 6 from both sides:
\( 114 - 6 = 3w \)
\( 108 = 3w \)
Divide both sides by 3:
\( w = \frac{108}{3} = 36 \)

Step4: Find the length

The length is \( 2w + 6 \). Substitute \( w = 36 \):
\( 2\times36 + 6 = 72 + 6 = 78 \)

Answer:

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