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

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