# Thread: Fun word problems

1. ## Fun word problems

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 ${w}$ be the length of the pen perpendicular to the barn. Write an equation to model the area of the pen in terms of ${w}$.

2. 125 perpendicular and 250 parallel

3. 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.

4. 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.