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    Subject

    Quantitative Aptitude

    Topic

    Areas & Volumes

    If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.

    ক)
    20
    খ)
    40
    গ)
    50
    ঘ)
    90

    Explanation

    Let x and y be the length and breadth of the rectangle respectively. Then, x - 4 = y + 3 or x - y = 7 ----(i) Area of the rectangle =xy; Area of the square = (x - 4) (y + 3) (x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(ii) Solving (i) and (ii), we get x = 16 and y = 9. Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.

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