the perimeter of a rectangular herb garden is 74 feet. If the length of the garden is 5 feet longer than 3 times its width, what is the garden's width?

Answer 1

To find the width of the rectangular herb garden, we'll use the information given:

1. The perimeter of the rectangular garden is 74 feet.
2. The length of the garden is 5 feet longer than 3 times its width.

Let's define:
- Width of the garden as \( W \) feet.
- Length of the garden as \( L \) feet.

From the problem, we know:
\[ L = 3W + 5 \]

The formula for the perimeter of a rectangle is:
\[ P = 2L + 2W \]

Substituting the given perimeter:
\[ 74 = 2L + 2W \]

Now, substitute \( L = 3W + 5 \) into the perimeter equation:
\[ 74 = 2(3W + 5) + 2W \]

Simplify the equation:
\[ 74 = 6W + 10 + 2W \]
\[ 74 = 8W + 10 \]

Subtract 10 from both sides:
\[ 64 = 8W \]

Divide by 8:
\[ W = 8 \]

So, the width of the garden is 8 feet. Let's verify by finding the length and checking the perimeter:
\[ L = 3W + 5 = 3(8) + 5 = 24 + 5 = 29 \]

Check the perimeter:
\[ P = 2L + 2W = 2(29) + 2(8) = 58 + 16 = 74 \]

The calculated perimeter matches the given perimeter. Therefore, the width of the garden is indeed 8 feet.