SSC CPO 2020 PYQ — Question 145

The correct answer is option 3 i.e. 120.

Side of rhombus = 13 cm

Length of diagonal AC = 10 cm

OC = 5 cm

Since the diagonals of a rhombus bisect each other at a right angle

So, △BOC is right-angled

Then, by Pythagoras' Theorem -

BC² = OC² + OB²

13² = 5² + OB²

OB² = (169 - 25) = 144

OB = $\sqrt144$​ = 12cm

Hence, diagonal (BD) = 2 × OB = 2 × 12 = 24 cm

Area of rhombus = (1/2)​ × d₁​ × d₂ ​= (1/2)​ × 10 × 24 = 120 cm²