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

User Stursby
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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


User Willurd
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