Question

Each side of a rhombus is 13 cm and one diagonal is 10 cm. Find

(i) the length of its other diagonal
(ii) the area of the rhombus

please solve this question​

Answer 1

Answer:

(i) 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 rt. angled.

Then, by Pythagoras Theorem we have

BC2 = OC2 + OB2

132 = 52 + OB2

OB2 = 169 – 25 = 144

⇒ OB = √144 = 12 cm

Hence,

Diagonal BD = 2 × OB = 2 × 12 = 24 cm

(ii) Area of rhombus = ½ × d1 × d2

= ½ × 10 × 24 = 120cm2