# Find the diagonal of a rectangle if its perimeter is 62cm, and the distance from the point of intersection

**Find the diagonal of a rectangle if its perimeter is 62cm, and the distance from the point of intersection of the diagonals to one of the sides is 12cm.**

If the perimeter of the rectangle is 62 cm, then the sum of the lengths of two adjacent sides is 62/2 = 31 cm.

The distance from the point of intersection of the diagonals to one of the sides is equal to half the length of the other side. Therefore, one of the sides of the rectangle is 12 x 2 = 24 cm, then the other will be 31-24 = 7 cm.

The adjacent sides of the rectangle are the legs of the right triangle, and the diagonal of the rectangle is the hypotenuse. According to the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse.

7 ^ 2 + 24 ^ 2 = 49 + 576 = 625. We extract the square root of 625, we get the length of the hypotenuse – 25 cm.

We got the diagonal of the rectangle – 25 cm.