the perimeter of a regulation tennis court is 228 feet. If the length of a tennis court is 6 feet longer than twice the width, how wide is a regulation tennis court?

Answer 1

Let's denote the width of the tennis court as \( w \) feet. According to the problem, the length \( l \) of the tennis court is 6 feet longer than twice the width. Therefore, we can write the length as:

\[ l = 2w + 6 \]

We are also given that the perimeter of the tennis court is 228 feet. The formula for the perimeter \( P \) of a rectangle is given by:

\[ P = 2l + 2w \]

Substituting the given perimeter value:

\[ 228 = 2l + 2w \]

Now, substituting the expression for \( l \) into the perimeter equation:

\[ 228 = 2(2w + 6) + 2w \]

First, distribute the 2 inside the parentheses:

\[ 228 = 4w + 12 + 2w \]

Combine like terms:

\[ 228 = 6w + 12 \]

Subtract 12 from both sides to isolate the term with \( w \):

\[ 216 = 6w \]

Now, solve for \( w \) by dividing both sides by 6:

\[ w = \frac{216}{6} \]
\[ w = 36 \]

Therefore, the width of a regulation tennis court is 36 feet.