Question

if the area of a given rhombus is 45 cm square, find the value of x. one is x cm and another 10 cm

Answer 1

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 △AOB, AB=10 cm, AO=8 cm

By Pythagoras theorem, AB

2

=AO

2

+BO

2

⇒10

2

=8

2

+BO

2

⇒BO

2

=100−64=36

∴BO=6cms

Diagonal BD=2×6=12cm

Area of Rhombus=

2

1

×(productofthediagonals)

=

2

1

×16×12=8×12=96sq.cm

Hence length of other diagonal =12 cm;

And Area of rhombus =96sq.cm