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    Question

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

    25 cm, is 66 cm. If the length of a rectangle is 10 cm more than the arc subtended by the sector and its perimeter is 84 cm, then find the area (in cm2) of the rectangle.
    A 400 Correct Answer Incorrect Answer
    B 415 Correct Answer Incorrect Answer
    C 416 Correct Answer Incorrect Answer
    D 426 Correct Answer Incorrect Answer
    E None of these 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) = 66 Or, l = 66 – 2r = 66 – (2 × 25) = 16 cm Therefore, length of the rectangle = 16 + 10 = 26 cm Let the breadth of the rectangle be ‘b’ cm Therefore, 2 × (26 + b) = 84 Or, b = 42 – 26 = 16 cm Therefore, area of the rectangle = length × breadth = 26 × 16 = 416 cm2

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