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Of all rectangles with a perimeter of 12 which one has the maximum area

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shubhamchouhanvrVT

The rectangle maximum area will be A=9 square units with the length=3 and the width=3.

What is area of rectangle?

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.

To know more about area of rectangle follow

https://brainly.com/question/25292087

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