Question

Each sides of a rhombus is 13cm and one diagonal is 10cm. Find:
(i) the length of its other diagonal
(ii) the area of the rhombus

❌❌Don't Spam ❌❌​

Answer 1

Answer:

Given

Side of rhombus =13 cm

Length of diagonal AC=10 cm

∴ OC=5 cm

Since, the diagonals of a rhombus bisect each other at right angles.

So, △BOC is right-angled.

Then, by Pythagoras Theorem we have

BC

2

=OC

2

+OB

2

⇒13

2

=5

2

+OB

2

⇒OB

2

=169−25=144

⇒OB=

144

=12cm

Hence,

diagonal BD=2×OB=2×12=24 cm

(ii) Area of rhombus =

2

1

×d

1

×d

2

=

2

1

×10×24=12 cm

2

Answer 2

Answer:

Rhombus ABCD with centre O,

side (S) = 13 cm

shorter diagnol (P) = 10 cm

consider triangle OCB,

applying Pythagoras theorem,

OC = √ (BC^2 - OB^2 ) = √(169 - 25) = √ 144 = 12

OC = 12 cm

longer diagnol (AC) = AO + OC = 2OC = 2 x 12 = 24

Longer diagnol, AC = 24 cm.

Area of rhombus ABCD = [(AC x BD) / 2 ] = 10 x 24 / 2

Area of Rhombus ABCD = 120 sq.cm

HOPE IT HELPS YOU