Let’s denote the length of the base of the parallelogram as $b$.

The area of a parallelogram is given by the formula $A = bh$, where $A$ is the area, $b$ is the base, and $h$ is the height.

The area of the square is equal to the area of the parallelogram, so we can set up the equation:

$A_{\text{square}} = A_{\text{parallelogram}}$

The area of the square is given by the formula $A_{\text{square}} = s^2$, where $s$ is the side length of the square.

The perimeter of the square is given by the formula $P_{\text{square}} = 4s$, where $P_{\text{square}}$ is the perimeter of the square.

We are given that the perimeter of the square is 100 m, so we can set up the equation:

$100 = 4s$

Solving for $s$, we find that $s = 25$ m.

Since the square is a special type of parallelogram, we know that the opposite sides are equal in length. Therefore, the base of the parallelogram is also 25 m.

So, the length of the corresponding base of the parallelogram is 25 m.