Sum of the diagonals of a rhombus is 70 cm. Side of the rhombus is 25 cm. What is the area (in square cm) of the rhombus?
Show answer & explanation
Correct answer: B
Explanation
Given:
Sum of diagonals = 70 cm, Side = 25 cm.
According to the formula:
In a rhombus, (d₁/2)² + (d₂/2)² = Side²
Area = (d₁ × d₂) / 2
Let d₁ = x, d₂ = 70 − x
(x/2)² + ((70 − x)/2)² = 25²
x² + (70 − x)² = 2500
x² + 4900 − 140x + x² = 2500
2x² − 140x + 4900 = 2500
2x² − 140x + 2400 = 0
x² − 70x + 1200 = 0
(x − 30)(x − 40) = 0
d₁ = 30, d₂ = 40
Area = (30 × 40) / 2 = 600 sq. cm.