125 perpendicular and 250 parallel
Ben wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Ben has 500 feet of fencing, what dimensions would maximize the area of the pen?
Let be the length of the pen perpendicular to the barn. Write an equation to model the area of the pen in terms of .
i figured out the area i just need help with writing the equation to get there
A=.... In terms of W.
I was thinking that:
500=2L+2W
500-2W=2L
250-W=L
Since A=L*W
A=W(250-W)
A=250W-2W^2
but it doesn't take into account that one side is already covered by the barn.
what if u used the equation for perimeter first excluding the length of the barn something like 2*w+L. because one Length is the barn. when that equation = 500 then maybe u will have the correct dimensions. It's been awhile since I've done this kind of work though.