If a side of a rhombus is 10 cm and one of the diagonals is 16 cm, find the other diagonal.

Let ABCD be the rhombus and the diagonals intersect at point O.

Let diagonal AC = 16 cm.

We know that,

Diagonals of rhombus bisect each other at right angles.

∴ AO = OC = $\dfrac{AC}{2} = \dfrac{16}{2}$ = 8 cm and BO = OD = x cm (let).

In right angle triangle AOB,

By pythagoras theorem,

⇒ (Hypotenuse)² = (Perpendicular)² + Base²

⇒ AB² = AO² + OB²

⇒ 10² = 8² + x²

⇒ 100 = 64 + x²

⇒ x² = 100 - 64

⇒ x² = 36

⇒ x = $\sqrt{36}$ = 6 cm.

From figure,

⇒ BD = BO + OD = 6 + 6 = 12 cm.

Hence, length of other diagonal = 12 cm.