Question
A rhombus has diagonals in the ratio 4:3 and an area of
2,400 cm². A circle is drawn using the smaller diagonal of the rhombus as its diameter. What is the difference between the area of this circle and 75% of the area of the rhombus? (Take π = 3)Solution
ATQ,
Let the diagonals be 4x and 3x.
Area = (1/2) × 4x × 3x = 6x²
2400 = 6x² → x² = 400 → x = 20
Smaller diagonal = 3x = 60 cm → diameter of circle = 60 cm
Radius = 30 cm → Area = 3 × 30² = 3 × 900 = 2700 cm²
75% of rhombus = 0.75 × 2400 = 1800 cm²
Difference = 2700 - 1800 = 900 cm²
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