2026 · Q52
The area of a rhombus is 720 cm² and the sum of its diagonals is 98 cm. What is the perimeter of the rhombus?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A160 cm
- B164 cm
- C168 cm
- D172 cm
Explanation
With diagonals d₁, d₂: d₁ + d₂ = 98 and area d₁d₂/2 = 720 gives d₁d₂ = 1440. Then d₁² + d₂² = (d₁ + d₂)² − 2d₁d₂ = 9604 − 2880 = 6724. Each rhombus side satisfies side² = (d₁/2)² + (d₂/2)² = 6724/4 = 1681, so side = 41 and the perimeter is 164 cm, option B.