The diagonals of a rhombus are 24cm and 10cm Find the perimeter of the rhombus - Maths - Surface Areas and Volumes

Question

The diagonals of a rhombus are 24cm and 10cm Find the perimeter of
the rhombus

Varun.Rawat · Accepted Answer

Let ABCD be the rhombus in which AC and BD are the diagonals
Now, AC = 24 cm; BD = 10 cmWe know that, diagonals of a rhombus bisect each other at right angle
Now, OA = OC = 12 cm and OB = OD = 5 cmAlso, ∠AOB = ∠BOC = ∠COD = ∠DOA = 90°In ∆AOB,   AB2 = OA2+OB2  Pythagoras theorem⇒AB2 = 122 + 52⇒AB2 = 144+25⇒AB2 = 169⇒AB = 13 cmNow, perimeter of ABCD = 4AB = 4×13 = 52 cm

The diagonals of a rhombus are 24cm and 10cm .Find the perimeter of the rhombus