Given that half of the perimeter of a rectangular garden is 36 m, we can set up the following equation for the perimeter \( P \):
\[ P = 2 \times 36 = 72 \text{ m} \]
The formula for the perimeter of a rectangle is:
\[ P = 2 \times (\text{Length} + \text{Width}) \]
Let the width of the garden be \( w \) meters. According to the problem, the length \( l \) of the garden is 4 meters more than the width:
\[ l = w + 4 \]
Substituting the expression for the length into the perimeter formula:
\[ 72 = 2 \times (w + (w + 4)) \]
Simplifying the equation:
\[ 72 = 2 \times (2w + 4) \] \[ 72 = 4w + 8 \]
Now, let's isolate \( w \):
\[ 72 - 8 = 4w \] \[ 64 = 4w \] \[ w = \frac{64}{4} = 16 \text{ m} \]
Now substituting \( w = 16 \) back into the equation for the length:
\[ l = w + 4 = 16 + 4 = 20 \text{ m} \]
Thus, the dimensions of the garden are:
- Width: \( 16 \text{ m} \)
- Length: \( 20 \text{ m} \)
Final answer:
- Length = 20 m
- Width = 16 m