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    Question

    The length of a rectangle is 8 cm less than the radius

    of a circle. The perimeter of the rectangle is 60 cm, and the ratio of its length to breadth is 4:2. Find how much greater the area of the circle is than the area of the rectangle.
    A 2264 cm² Correct Answer Incorrect Answer
    B 1427 cm² Correct Answer Incorrect Answer
    C 2335 cm² Correct Answer Incorrect Answer
    D 2465 cm² Correct Answer Incorrect Answer

    Solution

    ATQ, Let the length and breadth of the rectangle be 4a cm and 2a cm, respectively. Perimeter of the rectangle = 2 × (Length + Breadth) 60 = 2 × (4a + 2a) 60 = 2 × 6a 60 = 12a a = 5 Length of the rectangle = 4a = 4 × 5 = 20 cm Breadth of the rectangle = 2a = 2 × 5 = 10 cm Given length is 8 cm less than the radius, Radius of the circle = 20 + 8 = 28 cm Area of the circle = πr² = 22/7 × 28 × 28 = 2464 cm² Area of the rectangle = 20 × 10 = 200 cm² Required difference = 2464 − 200 = 2264 cm²

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