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3 February, 03:28

If the perimeter of a rectangle is 46 cm and the area is 132 square cm, then what are the dimensions of the rectangle?

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  1. 3 February, 07:03
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    Let the length be l and the width be w

    Perimeter will be:

    P=2 (l+w) = 46

    thus

    l=23-w ... i

    the area will be:

    A=l*w=132

    hence

    l=132/w ... ii

    combining i and ii we get:

    23-w=132/w

    this will be written as:

    w (23-w) = 132

    23w-w^2=132

    hence:

    w^2-23w+132=0

    solving the quadratic above we obtain:

    (w-11) (w-12) = 0

    hence:

    width, w=11 or 12

    thus

    length=132/11 or 132/11

    =12 or 11
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