To find the perimeter of a garden with a given area, we need to know the dimensions (length and width) of the garden. The area of a rectangle (which we will assume your garden is) is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
Given that the area is 132 square feet, we can express the width (W) in terms of the length (L):
\[ W = \frac{132}{L} \]
The perimeter (P) of a rectangle is given by the formula:
\[ P = 2 \times (L + W) \]
Substituting for W:
\[ P = 2 \times \left(L + \frac{132}{L}\right) \]
To determine the dimensions that give a particular perimeter, you could pick any positive value for L and compute W and P. However, if you're looking for the optimal square garden, using equal sides would minimize the perimeter for a given area.
We can find the dimensions of the square garden by taking the square root of the area:
\[ L = W = \sqrt{132} \approx 11.49 \text{ feet} \]
Now, calculate the perimeter:
\[ P = 4 \times L = 4 \times \sqrt{132} \approx 4 \times 11.49 \approx 45.96 \text{ feet} \]
If your garden is rectangular and you use different values for L and W (as long as their product equals 132), the perimeter will vary.
In conclusion, without fixed dimensions, the perimeter can vary. The perimeter of a square garden with an area of 132 square feet is approximately 45.96 feet. Depending on how you want to shape your garden, you can choose different combinations of length and width to get the perimeter based on your requirement.