Question

Each side of a rhombus is 10 cm. long and one of its diagonal is 16 cm. Find

the length of other diagonal and hence find the perimeter of the rhombus.​

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Each side of a rhombus is 10 cm long and one of its diagonals measures 16 cm. Find the length of the other diagonal and hence find the area of the rhombus.

Asked by Topperlearning User | 17th Aug, 2017,  07:22: AM

Expert Answer:

Diagonals of a rhombus bisect each other at right angles.

Let ABCD be the rhombus, Diagonal AC= 16 cm and side AB = 10 cm.

In right triangle AOB, AB = 10 cm, AO = 8 cm

By Pythagoras theorem, AB2 = AO2 + BO2

(10)2 = (8)2 + BO2

BO2 = (10)2 – (8)2

BO = 6 cm

Diagonal BD = 2 x 6 = 12 cm

Hence length of other diagonal = 12 cm; Area of rhombus = 96 cm2