Sum of the diagonals of a rhombus is 62 cm. Area of this rhombus is 336 square cm. What is the side (in cm) of the rhombus?
Show answer & explanation
Correct answer: C
Explanation
Let the diagonals of the rhombus be d₁ and d₂.
Given:
d₁ + d₂ = 62 cm
Area of rhombus = 336 cm²
Formula:
Area = 1/2 × d₁ × d₂
1/2 × d₁ × d₂ = 336
d₁ × d₂ = 672
Now,
x² - (Sum of diagonals)x + (Product of diagonals) = 0
x² - 62x + 672 = 0
(x - 48)(x - 14) = 0
Therefore, diagonals are:
d₁ = 48 cm, d₂ = 14 cm
Half of diagonals:
48/2 = 24 cm
14/2 = 7 cm
Side of rhombus = √(24² + 7²)
= √(576 + 49)
= √625
= 25 cm
Answer: 25 cm