SSC CPO 2022 PYQ — Question 129

The correct answer is option 2 i.e.  $1\over 4$(L² - 4P²)

If the sum of the diagonals of a rhombus is L and  the perimeter is 4P

As we know

d₁² + d₂² = 4 P²

where d₁ and d₂ are diagonals of a rhombus and P is a side of a rhombus

Given that

d₁ + d₂  = L

And the side of the rhombus = P

Calculation

d₁² + d₂² = 4 P²

L² - 2d₁d₂  = 4 P²

2d₁d₂ = L² - 4P²

The area of the rhombus = d₁d₂/2

Hence, The area =  $1\over 4$(L² - 4P²)