Question

    The ratio of radius of a circle and side of a square is

    in the ratio 7:8 respectively. The perimeter of the square is 20 meters more than the perimeter of a rectangle whose area is 120 metre2 . If the ratio of length and breadth of rectangle is 6:5, then find the area of circle.
    A 616 sq m Correct Answer Incorrect Answer
    B 346 sq m Correct Answer Incorrect Answer
    C 626 sq m Correct Answer Incorrect Answer
    D 516 sq m Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the length and the breadth of the rectangle be 6x metres and 5x metres respectively.Area of the rectangle = length X breadthATQ,6x X 5x = 120Or, x 2  = 4Or, 'x' = 2So, the perimeter of the rectangle = 2 X (length + breadth)So, 2 X (2 X 6 + 2 X 5) = 2 X 22 = 44 metresSo, the perimeter of the square = 44 + 20 = 64So, side of the square = (64/4) = 16 metresSo, the radius of the circle = (16/8) X 7 = 14 metresSo, required area = π X radius 2  = (22/7) X 14 X 14 = 616 m 2

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