A square and a rectangle have the same area. If the rectangle has a length of 25 cm and a perimeter of 82 cm, find the length of the square.

First find the area of the rectangle. Since two sides of the rectangle are the same (25cm), we will subtract 50 from the perimeter: 82 - 50 = 32

So the length of the other two sides of the rectangle total 32 cm. To find the length of each of the two sides, divide 32 into 2: 32/2 = 16.

So the width of the rectangle is 16cm and the length is 25 cm. Now find the area: 16 * 25 = 400

Now that we know the area of the rectangle, and we know that it is the same as the square, let's find the side lengths of the square by finding the square root of 400. You can do this with a calculator: 20

The square root of 400 is 20, so the side lengths of the square is 20cm.