Let the width of the garden be \( w \) meters. Since the length is three times the width, we can express the length as \( l = 3w \).
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2(l + w) \]
Given that the perimeter is 96 meters, we can set up the equation:
\[ 2(l + w) = 96 \]
Substituting \( l = 3w \) into the perimeter equation:
\[ 2(3w + w) = 96 \]
This simplifies to:
\[ 2(4w) = 96 \]
\[ 8w = 96 \]
Now, we can solve for \( w \):
\[ w = \frac{96}{8} = 12 , \text{meters} \]
Now that we have the width, we can find the length:
\[ l = 3w = 3 \times 12 = 36 , \text{meters} \]
Thus, the dimensions of the garden are:
- Width: \( 12 \) meters
- Length: \( 36 \) meters
So, the final answer is:
- Length = 36 meters
- Width = 12 meters