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    Question

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

    17 cm, is 63 cm. If the length of a rectangle is 10 cm more than the arc subtended by the sector and its perimeter is 98 cm, then find the area (in cm2) of the rectangle.
    A 390 Correct Answer Incorrect Answer
    B 300 Correct Answer Incorrect Answer
    C 370 Correct Answer Incorrect Answer
    D 340 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the arc subtended by the sector be β€˜l’ cm and the radius of the circle be β€˜r’ cm According to the question, (l + 2r) = 63 Or, l = 63 – 2r = 63 – (2 Γ— 17) = 29 cm Therefore, length of the rectangle = 29 + 10 = 39 cm Let the breadth of the rectangle be β€˜b’ cm Therefore, 2 Γ— (39 + b) = 98 Or, b = 49 – 39 = 10 cm Therefore, area of the rectangle = length Γ— breadth = 10 Γ— 39 = 390 cm2

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