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    Question

    The length of a rectangle is 8 cm more than its breadth. If the area of the rectangle is 192 cm², determine the perimeter of the rectangle.

    A 24 cm Correct Answer Incorrect Answer
    B 64 cm Correct Answer Incorrect Answer
    C 34 cm Correct Answer Incorrect Answer
    D 27 cm Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the breadth of the rectangle be 'x' cm. Then, the length of the rectangle will be 'x + 8' cm. According to the given conditions, x(x+8) = 192 Or, x2 + 8x − 192=0

    Factoring the quadratic equation, x2 +16x − 8x − 192 = 0 Or, x(x+16) - 12(x+16) = 0 Or, (x-12)(x+16) = 0 So, x = 12 or x = −16 (not possible)

    Breadth of the rectangle = 12 cm Length of the rectangle = 12 + 8 = 20 cm Perimeter of the rectangle = 2(12+20) = 2×32 = 64 cm

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