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