Let the width of the recreational court be \( x \) feet. Since the length is three times the width, the length can be expressed as \( 3x \) feet.
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2(\text{length} + \text{width}) \]
Substituting the expressions for length and width into the perimeter formula, we have:
\[ 272 = 2(3x + x) \]
Simplifying the expression inside the parentheses:
\[ 272 = 2(4x) \]
This can be further simplified:
\[ 272 = 8x \]
Now, we solve for \( x \) by dividing both sides by 8:
\[ x = \frac{272}{8} = 34 \]
Thus, the width of the court is \( 34 \) feet. Now we can find the length:
\[ \text{length} = 3x = 3 \times 34 = 102 \text{ feet} \]
So, the dimensions of the court are:
- Width = \( 34 \) feet
- Length = \( 102 \) feet
To verify, we can check the perimeter:
\[ P = 2(\text{length} + \text{width}) = 2(102 + 34) = 2(136) = 272 \text{ feet} \]
Everything checks out, so the final dimensions of the court are:
\[ \text{Width} = 34 \text{ feet}, \quad \text{Length} = 102 \text{ feet} \]
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