Area of a rhombus is 840 square cm. Side of the rhombus is 37 cm. What is the sum (in cm) of its diagonals?
Show answer & explanation
Correct answer: D
Explanation
Area of the rhombus = (Diagonal₁ × Diagonal₂) / 2
Diagonal₁ × Diagonal₂ = 2 × 840 = 1680
Side = 37 cm
By Pythagoras theorem,
Diagonal₁² + Diagonal₂² = 4 × 37² = 5476
(Diagonal₁ + Diagonal₂)² = 5476 + 2 × 1680= 8836
Diagonal₁ + Diagonal₂ = √8836 = 94