Within a farmer's pastures, there is a one-acre tract of land shaped like a right triangle. At the midpoint of the hypotenuse is a post, to which a dog is tethered with just enough rope to reach the endpoints of the hypotenuse. There are also posts at the midpoints of the legs of the triangle; to each of which is tethered a sheep with just enough rope to reach the endpoints of its respective leg of the triangle.

How much space do the sheep have to graze in (collectively) without having to worry about the dog reaching them?

(In reply to not quite complete by Cory Taylor)

Cory,

I only object to your "not quite complete" description.

As you've agreed, my solution DOES answer the question.
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For anyone who wants to continue the tedium :-), you need only show that the two sheep's respective circles grow/shrink in size in proportion to the square of the growth/shrinking of the respective legs (from equality).

And similarly, the dog's portion of those circles grow/shrink accordingly.

I will leave it as an excersise to the reader (to the floobler?) to set up those equations and bring closure to any outstanding issues.
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Lastly, contrary to any impression I may have given above, I think this problem is definitely flooble-worthy, and I would rate it a 4 or a 5.

Cheers!

Posted by SilverKnight on 2003-11-12 15:06:22