Sum of the diagonals of a rhombus is 14 cm. Area of this rhombus is 24 square cm. What is the side (in cm) of the rhombus?
Show answer & explanation
Correct answer: B
Explanation
Sum of diagonals = 14 cm
Area = 24 sq cm
d₁ + d₂ = 14
Area of rhombus = 1/2 × d₁ × d₂
24 = 1/2 × d₁ × d₂
d₁ × d₂ = 48
d₁ = 6 cm, d₂ = 8 cm
The diagonals of a rhombus bisect each other at right angles.
Therefore, half-diagonals = 3 cm and 4 cm
Side = √(3² + 4²)
= √(9 + 16)
= √25
= 5 cm