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    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)
    A 480 cm² Correct Answer Incorrect Answer
    B 580 cm² Correct Answer Incorrect Answer
    C 825 cm² Correct Answer Incorrect Answer
    D 900 cm² Correct Answer Incorrect Answer

    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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