Question

One of the diagonals of a rhombus is thrice as the other. If the sum of the length of the diagonals is 24 cm, then find the area of the rhombus.

Answer 1

Let one of the diagonals of rhombus be ‘d₁’ cm and the other be d₂ cm.

Give d₁ = 3 × d₂

Also d₁ + d₂ = 24 cm

⇒ 3d₂ + d₂ = 24

4d₂ = 24

d₂ = `24/4`

d₂ = 6 cm

d₁ = 3 × d₂ = 3 × 6

d₁ = 18 cm

∴ Area of the rhombus = `1/2` × d₁ × d₂ sq.units

= `1/2` × 18 × 6 cm² 

= 54 cm²

Area of the rhombus = 54 cm²