A rhombus has diagonals in the ratio 7:24. If the side length is 25 cm, find the exact lengths of the diagonals and hence the area of the rhombus.
Show answer & explanation
Correct answer: B
Explanation
Given:
Ratio of diagonals = 7 : 24
Side of rhombus = 25 cm
By formula:
In rhombus
s² = (d₁/2)² + (d₂/2)²
Area = (d₁ × d₂) / 2
Calculation:
Let
d₁ = 7x
d₂ = 24x
25² = (7x/2)² + (24x/2)²
625 = (49x²/4) + (576x²/4)
625 = (625x²/4)
x² = 4
x = 2
d₁ = 14 cm
d₂ = 48 cm
Area = (14 × 48) / 2 = 336 cm²
Diagonals = 14 cm and 48 cm cm
Area = 336 cm²