The diagonals of a rhombus are 24 cm and 32 cm, then perimeter is?

The diagonal of a rhombus bisect each other perpendicularly.

Therefore, in Δ AOB:

⇒\(\angle\)AOB = 90°,

AO = \(\frac{AC}{2}\) = 12 and

BO = \(\frac{BD}{2}\) = 16

So,

⇒ AB² = OA² + OB²

⇒ AB² = (12)² + (16)²

⇒ AB² = 144 + 256 = 400

⇒ AB = 20

⇒ Perimeter = 4 × side = 4 × 20 = 80 cm