In a large and flat grass field, there is a 30x30 feet square barn facing due North. Straight from the NorthEast corner of the barn is a fence running due East 40 feet long. There is a horse tied on the SouthEast corner of the barn with a rope that will allow him to eat grass in any direction up to 100 feet. The horse can't eat under the barn, and the rope can't pass through the barn or through the fence. The horse can walk around the barn or the fence, but is limited by the length of the rope.
How many square feet of grass can the horse reach?
(I found this problem pretty interesting, but I am not the author and have no idea who is the author).
I agree with all the previous comments/solutions and I find them all very good (especially the pretty picture!)
However, all final answers so far have been given as decimal approximations to the exact value... as a want-to-be pure mathematician, I feel it necessary to include that exact value here. So, to wit, the horse can graze over
[ 7875pi + 600 + 400sqrt(6) + 3750arctan(3/4)
- 1250arctan(8sqrt(6)/29) - 800arctan(2sqrt(6)/5) ]
square feet of grass!!
So, now we can all use our own various number crunchers to get the correct answer to any required number of decimal places. Isn't that great?!?
-John
exact answer
