Question

A rectangular garden has a length that is three times its width. If the perimeter of the garden is 96 meters, find its length and width.

Answer 1

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