Answer:
Let's denote the side length of the square plot as \( x \). Since there is a 3-meter wide path surrounding it, the effective side length including the path would be \( x + 2 \times 3 \) (3 meters on each side).
So, the total area including the path is:
\[ \text{Total Area} = \text{Side Length Including Path} \times \text{Side Length Including Path} \]
\[ \text{Total Area} = (x + 2 \times 3) \times (x + 2 \times 3) \]
Given that the area of the path is 132 square meters, we can set up the equation:
\[ \text{Total Area} - \text{Area of the Path} = 132 \]
\[ (x + 2 \times 3) \times (x + 2 \times 3) - x \times x = 132 \]
Now, you can simplify and solve this quadratic equation to find the side length (\( x \)) of the square plot. Once you have \( x \), you can find the area of the square plot by squaring \( x \).
