The diagonals of the parallelogram are 3 dm and 5 dm, and one of its sides is 2√2 dm.

The diagonals of the parallelogram are 3 dm and 5 dm, and one of its sides is 2√2 dm. What is the side of a parallelogram that is not parallel to it?

Let us take the unknown side of the parallelogram equal to x. The sum of the squares of the diagonals is equal to the sum of the squares of the sides of the parallelogram, so we can write:
3 ^ 2 + 5 ^ 2 = x ^ 2 + x ^ 2 + (2√2) ^ 2 + (2√2) ^ 2;
9 + 25 = 2x ^ 2 + 2 * 4 * 2;
34 = 2x ^ 2 + 16;
2x ^ 2 = 34-16 = 18;
x ^ 2 = 18/2 = 9;
x = √9 = 3 dm.