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    Question

    The perimeter of a sector of a circle, whose radius is

    20 cm, is 60 cm. If the length of a rectangle is 10 cm more than the arc subtended by the sector and its perimeter is 66 cm, then find the area (in cm2) of the rectangle.
    A 70 Correct Answer Incorrect Answer
    B 80 Correct Answer Incorrect Answer
    C 90 Correct Answer Incorrect Answer
    D 50 Correct Answer Incorrect Answer

    Solution

    Let the arc subtended by the sector be ‘l’ cm and the radius of the circle be ‘r’ cm According to the question, (l + 2r) = 60 Or, l = 60 – 2r = 60 – (2 × 20) = 20 cm Therefore, length of the rectangle = 20 + 10 = 30 cm Let the breadth of the rectangle be ‘b’ cm Therefore, 2 × (30 + b) = 66 Or, b = 33 – 30 = 3 cm Therefore, area of the rectangle = length × breadth = 3 × 30 = 90 cm2

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