alleryOne side of a rhombus is 37 cm and its area is 840 cm². Find the sum of the lengths of its diagonals.
A84 cm
B47 cm
C42 cm
D94 cm
Answer & Solution
Correct answer: D. 94 cm
1. Area = ½ × d₁ × d₂ = 840, so d₁d₂ = 1680. Half-diagonals satisfy (d₁/2)² + (d₂/2)² = 37², so d₁² + d₂² = 5476.
2. (d₁ + d₂)² = d₁² + d₂² + 2d₁d₂ = 5476 + 3360 = 8836.
3. d₁ + d₂ = √8836 = 94 cm.
_Source: RRB Group D CEN-02/2018 PYQ, Q.46._
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