Three sides of a rectangular playing field are to be fenced with 400 m of fencing. Find the dimensions so that the area of the field will be a maximum.

Can any one solve this question?

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- April 8th 2008, 07:23 PMRainaCalculus is killing me!
Three sides of a rectangular playing field are to be fenced with 400 m of fencing. Find the dimensions so that the area of the field will be a maximum.

Can any one solve this question? - April 8th 2008, 07:27 PMMathstud28OK here you go
- April 13th 2008, 09:14 PMRaina
i noticed sth

when u slove 400-4y=0

u get 100

NOT 50...

any way thanks for ur time and help - April 14th 2008, 12:11 AMMoo
Hello,

Let x and y be the sides (don't know how to name it :D) such as the perimeter P is :

P=x+2y=400 (one side is missing) -> x=400-2y

Plus, we want the area be at its maximum. The area A is :

A=xy

-> A=(400-2y)y=-2y²+400y

If you derivate : A'=-4y+400 and if y<100, A' will be positive, if y>100, A' will be negative. So it firstly increases and then decreases.

y=100 is a maximum, and so x=400-200=200 :)