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27 September, 12:41

Find the length and width of a rectangle that has perimeter 24 meters and a maximum area.

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  1. 27 September, 12:49
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    Let the length of the rectangle = x

    since the perimeter is 24m then the width of rectangle is (12-x) m.

    the area of rectangle is:

    A=x * (12-x)

    A=-x^2+12x

    x=-12/-2 = 6:

    Since the length is 6m the width will be: 12-6=6m

    We conclude that this rectangle has the maximum area when its shape is square of side 6m.

    We find the value of area for x=6m:

    Area = 6^2 = 36M^2
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