Find the side of the rhombus if its diagonals are 30 cm and 40 cm.

Let’s use the picture to solve the problem.

By the property of rum, its diagonals intersect at right angles and are halved at the point of intersection.

Then:

AO = OC = AC / 2 = 30/2 = 15 cm.

BO = OD = BD / 2 = 40/2 = 20 cm.

Consider a right-angled triangle AOB, in which the angle AOB = 90, leg AO = 15 cm, leg BO = 20 cm, and the hypotenuse AB is the side of the rum.

Let us find the hypotenuse AB by the Pythagorean theorem.

AB ^ 2 = AO ^ 2 + BO ^ 2 = 15 ^ 2 + 20 ^ 2 = 225 + 400 = 625.

AB = 25 cm.

Answer: The side of the rhombus is 25 cm.