Question
The area of a rhombus is 1,600 cm², and the lengths of its
diagonals are in the ratio 5:4. A circle is constructed with the smaller diagonal as the diameter. Find the difference between the area of the circle and 75% of the rhombus's area. (Take π = 3)Solution
ATQ,
Let diagonals = 5x and 4x
Area = (1/2) × 5x × 4x = 10x²
1600 = 10x² → x² = 160 → x = √160 ≈ 12.65
Smaller diagonal = 4x ≈ 50.6 cm
Radius ≈ 25.3 cm
Area of circle ≈ 3 × (25.3)² ≈ 3 × 640 ≈ 1920 cm²
75% of rhombus = 0.75 × 1600 = 1200 cm²
Difference ≈ 1920 - 1200 = 720 cm²
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