In a rhombus, the diagonals are in the ratio 8:15. If the side of the rhombus is 17 cm, determine the exact lengths of both diagonals and the area.
Show answer & explanation
Correct answer: C
Explanation
Given:
Ratio of diagonals = 8 : 15
Side of rhombus = 17 cm
By formula:
In rhombus
s² = (d₁/2)² + (d₂/2)²
Area = (d₁ × d₂) / 2
Let
d₁ = 8x
d₂ = 15x
s² = (d₁/2)² + (d₂/2)²
17² = (8x/2)² + (15x/2)²
289 = (4x)² + (7.5x)²
289 = 16x² + 56.25x²
289 = 72.25x²
x² = 4
x = 2
d₁ = 16 cm
d₂ = 30 cm
Area = (16 × 30) / 2 = 240 cm²
Diagonals = 16 cm and 30 cm
Area = 240 cm²