The perimeter of a rhombus is 60 cm. If one of its diagonals is 18 cm long, find (i) the length of the other diagonal, and (ii) the area of the rhombus.

Question

Philoid · Accepted Answer

Given:

Perimeter of rhombus = 60 cm

Length of diagonal 1 (d₁) = 18 cm

Let, Length of diagonal 2 be d₂

(i) Perimeter of rhombus = 4 × side

⇒ 60 = 4 × side

Now,

Side of rhombus = 1/2 × √(d₁² + d₂²)

⇒ 15 = 1/2 × √(18² + d₂²)

⇒ 15 = 1/2 × √(324 + d₂²)

⇒ 15 × 2 = √(324 + d₂²)

⇒ 30 = √(324 + d₂²)

Squaring both sides,

⇒ 900 = 324 + d₂²

⇒ 900-324 = d₂²

⇒ d₂² = 576

⇒ d₂ = 24

Therefore,

Length of other diagonal = 24 cm

(ii) Area of rhombus = 1/2 × d₁ × d₂

= 1/2 × 18 cm × 24 cm

= 216 cm²