The side of the rhombus is 15 cm, and one of its diagonals is 24 cm. Find the other diagonal of this rhombus.

The diagonals of the rhombus intersect and the intersection point is halved. The diagonals of the rhombus intersect at right angles. The side of the rhombus, half of the first diagonal and half of the second diagonal form a right-angled triangle. In this triangle, the side of the rhombus a = 15 cm is the hypotenuse, half of the first diagonal d1 / 2 = 24/2 = 12 cm is the leg, half of the second diagonal d2 / 2 is also the leg.

We apply the Pythagorean theorem to this right-angled triangle: The square of the hypotenuse is equal to the sum of the squares of the legs.

(d1 / 2) ^ 2 + (d2 / 2) ^ 2 = a ^ 2;

(d2 / 2) ^ 2 = a ^ 2 – (d2 / 2) ^ 2;

(d2 / 2) ^ 2 = 15 ^ 2 – 12 ^ 2 = 225 – 144 = 81;

d2 / 2 = √81 = 9 (cm).

Let’s find the diagonal. It is 2 times more than half of the diagonal.

d2 = 9 * 2 = 18 (cm).

Answer. 18 cm.