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    Question

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

    22 cm, is 64 cm. If the length of a rectangle is 10 cm more than the arc subtended by the sector and its perimeter is 80 cm, then find the area (in cm2) of the rectangle.
    A 310 Correct Answer Incorrect Answer
    B 320 Correct Answer Incorrect Answer
    C 300 Correct Answer Incorrect Answer
    D 330 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) = 64 Or, l = 64 – 2r = 64 – (2 Γ— 22) = 20 cm Therefore, length of the rectangle = 20 + 10 = 30 cm Let the breadth of the rectangle be β€˜b’ cm Therefore, 2 Γ— (30 + b) = 80 Or, b = 40 – 30 = 10 cm Therefore, area of the rectangle = length Γ— breadth = 10 Γ— 30 = 300 cm2

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