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    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)
    A 480 cm² Correct Answer Incorrect Answer
    B 580 cm² Correct Answer Incorrect Answer
    C 325 cm² Correct Answer Incorrect Answer
    D 720 cm² Correct Answer Incorrect Answer

    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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