The length of the diagonals of a rhombus is 42 cm and 40 cm. Find the perimeter of the rhombus.

AC and BD are the diagonals of a rhombus ABCD.

Since the diagonals of a rhombus bisect at the right angle.

AC = 40 cm

AO =  = 20 cm

BD = 42 cm

OB = 42/2 = 21 cm

In right angled triangle AOB, we have

AO² + OB² = AB²

⇒ 20² + 21² = AB²

⇒ 400 + 441 = AB²

⇒ 841 = AB²

⇒ AB = √841 = 29 cm.

Perimeter of the rhombus = 4 × side = 4 × 29 = 116 cm

Hence, the required perimeter = 116 cm