Let’s denote the length of the side of the square as “s” and the length of the corresponding base of the parallelogram as “b”.

The area of a square is given by the formula A = s^2. The area of a parallelogram is given by the formula A = base * height.

Since the area of the parallelogram and the square are the same, we can set up the following equation:

s^2 = b * 15

We are also given that the perimeter of the square is 100 m, which means that the sum of all four sides of the square is 100 m. Since a square has four equal sides, each side of the square is 100/4 = 25 m.

Substituting this value into the equation, we have:

(25)^2 = b * 15 625 = 15b b = 625/15 b = 125/3

Therefore, the length of the corresponding base of the parallelogram is 125/3 m.