Find the side of the rhombus if you know that its diagonals are 24cm and 32cm

The diagonals of the rhombus intersect at right angles and are halved at the intersection. This means that the half of the diagonals and the side of the rhombus form a right-angled triangle, in which the halves of the diagonals are legs, the side of the rhombus is the hypotenuse. By the Pythagorean theorem:

a ^ 2 = (d1 / 2) ^ 2 + (d2 / 2) ^ 2 = (24/2) ^ 2 + (32/2) ^ 2 = 12 ^ 2 + 16 ^ 2 = 144 + 256 = 400.

a = √400 = 20 cm – rhombus side.