Let the width of the rectangular deck be \( w \) feet. According to the problem, the length \( l \) is three times the width:
\[ l = 3w \]
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2l + 2w \]
We know the perimeter is 96 feet, so we can set up the equation:
\[ 2l + 2w = 96 \]
Substituting \( l \) with \( 3w \):
\[ 2(3w) + 2w = 96 \]
This simplifies to:
\[ 6w + 2w = 96 \]
Combining like terms gives:
\[ 8w = 96 \]
Now, solve for \( w \):
\[ w = \frac{96}{8} = 12 \text{ feet} \]
Now, we'll find the length \( l \) using \( l = 3w \):
\[ l = 3(12) = 36 \text{ feet} \]
Thus, the dimensions of the rectangular deck are:
- Width: \( 12 \) feet
- Length: \( 36 \) feet