Question

There are 4 rectangular corrals of identical dimensions along the back wall of an existing barn using 200 ft of fencing.

The diagram has 4 rectangular corrals attached together but fencing is not needed on the back wall of the barn. The barn is above the 4 rectangular corrals.

I have x (front to back) as the length and y as the width. I am trying to figure out the function and dimensions (lxw) that will produce 4 corrals with a combined area of 1,680 ft^2 (give both solutions).

I came up with 200=5x+8y. I am not sure if it is right to start out.

Answer 1

let the corrals be depth d, width w.

so you have five d lengths, and four w lengths.

200=5d+4w I wonder why you thougth eight w, the barn is the back side.
1680=4dw
200=5d+4w or 4w=200-5d

1680=d(200-5d) or

5d^2-200d+1680=0
d^2-40d+336=0
(d -28 ) (d-12 )=0

d=28, w=15
d=12, w=35

check it.