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.
​

Answer 1

Step-by-step explanation:

Each side of a rhombus is 13cm and one diagonal is 10cm. What is the length of its other diagonal and the area of the rhombus?

From the question,

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

Answer 2

(i) Given,

Side of rhombus = 13 cm.

Length of diagonal AC = 10 cm.

∴ OC = 5 cm.

Since, the diagonals of 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 = 1/1 × d1 × d2

= 1/2 × 10 × 24 = 120cm²

${\fcolorbox{blue}{black}{\orange{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: DecentMortal\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}$