Let's translate this word problem into math!
We are told that both the rectangle and the square have the same perimeter.
If we call the length of the rectangle "L1", the width of rectangle "W1", and the length/width of the square "X", then we can translate our word problem like this:
2*L1 + 2*W1 = 4*X, since the perimeter of a rectangle is length + length + width + width.
We are told that the dimensions of the rectangle are 15 by 25. Since it doesn't matter, let's call L1 = 15 and W1 = 25. Now, we can use these values to figure out what X is, based on the equation we wrote!
2*15 + 2*25 = 30 + 50 = 80 = 4*X
So, 4*X = 80 --> X = 20
Since, we said that X represented the length of one side of the square, then to answer the question in the problem, the length of one side of the square is 20.
I hope this was helpful to you!