Question

The area of a rhombus is 64 cm2
. If one of its diagonals measures 16 cm, find the length of other diagonal.

Answer 1

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 △AOB, AB=10 cm, AO=8 cm

By Pythagoras theorem, AB2=AO2+BO2

⇒102=82+BO2

⇒BO2=100−64=36

∴BO=6cms

Diagonal BD=2×6=12cm

Area of Rhombus=21×(productofthediagonals)

=21×16×12=8×12=96sq.cm

Hence length of other diagonal =12 cm; 

And Area of rhombus =96sq.cm