Question

The lengths of the diagonals of a rhombus are 24 cm and 10 cm. Find each side of the rhombus.

Answer 1

We have,

ABCD is a rhombus with diagonals AC = 10 cm and BD = 24 cm

We know that diagonal of a rhombus bisect each other at 90°

∴ AO = OC = 5 cm and BO = OD = 12 cm

In ΔAOB, by Pythagoras theorem

AB² = AO² + BO²

⇒ AB² = 5² + 12²

⇒ AB² = 25 + 144 = 169

⇒ AB = `sqrt169` = 13 cm