SSC CPO 2023 PYQ — Question 124

The correct answer is option 1 i.e. 120 cm².

Given that

The perimeter of the rhombus is 52 cm

One of its diagonals is 10 cm long

Area of rhombus = ½ × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals

Perimeter of rhombus =  2√(d₁² + d₂²)

According to the question

⇒ 2√(d₁² + d₂²) = 52

⇒ (d₁² + d₂²) = 26² = 676

⇒ d₁² + 100 = 676

⇒ d₁² = 676 - 100 = 576 cm

⇒ d₁ = 24 cm

Hence, Area of the rhombus = 24 × 10/2 = 120 cm²