A horse breeder wants to construct a corral next to a horse barn that is L=20 feet long, using the barn as part of one side of the corral as shown in the figure above. The breeder has 320 feet of fencing available.

Answer 1

If the corral has dimensions x and y, with the barn as a part of side y, then

2x+2y-20 = 320

There are lots of values for x and y that fit that requirement. If y is the long side, then we just need x+y=150, so any value of y between 75 and 150 will work fine, but some of the corrals will be long and thin!

I expect the unseen figure puts further constraints on x and y.