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The rectangle maximum area will be A=9 square units with the length=3 and the width=3.
Area is defined as the space occupied by a plane or rectangle having length and width in two dimensional plane.
It is given that the perimeter of rectangle is P=12
So from the formula of perimeter of rectangle
2(L+W)=12
L+W=6
L=6-W
Now the area of rectangle will be
A=LxW
A=(6-W)W
Now for maximum area we will find the derivative and equate to zero.
[tex]A=(6W-W^2})[/tex]
[tex]A'=6-2W=0[/tex]
[tex]W=3[/tex]
[tex]L=6-W=6-3=3[/tex]
So the area will be
[tex]A=3\times 3=9 \ square \ units[/tex]
Hence the rectangle maximum area will be A=9 square units with the length=3 and the width=3.
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