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?
Hello,
Let x and y be the sides (don't know how to name it ) 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