Question

Each side of a rhombus is 61 cm and one of its diagonals is 22 cm long. Find (1) the length of the other diagonal and (ii) the area of the rhombus. The base of a triangle is 24 m and the remonding altitude is 16 cm. The area of the rhombus
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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

Answer 2

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 AAOB, AB 10 cm, AO = 8 cm

By Pythagoras theorem, AB? = AO + BO

10 82 + BO2

BO = 100 64 36

BO 6cms

Diagonal BD = 2 x 6= 12cm

Area of Rhombus=½× (product of the diagonals)

= ½x 16x 12= 8 x 12 = 96sq.cm

Hence length of other diagonal = 12 cm;

And Area of rhombus = 96sq.cm.