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

Let’s denote our rhombus ABCD, the diagonals intersect at point O and divide it into four equal right-angled triangles. In solving the problem, we will use the property of rhombus diagonals.
Consider a right-angled triangle AOB, in which the following are known:
hypotenuse AB = 15 cm (by condition);
leg AO = 1/2 AC = 1/2 * 24 = 12 (cm).
By the Pythagorean theorem, we find the second leg:
ОВ = √ (AB² – AO²) = √ (225 – 144) = √81 = 9 (cm).
Find the second diagonal:
BD = 2 * OB = 2 * 9 = 18 (cm).
Answer: the second diagonal is 18 cm.