My first thought was 3 solutions, then I realized two of them are the same. I figured I would post before looking at all the comments.
C can form either the right angle or one of the others.
Right angle not at C: (20 + c)^2 + (30 + c)^2 = 50^2
yields the positve solution c=10 for a (30,40,50) right triangle.
Right angle at C: 50^2 + (20 + x)^2 = (30 + x)^2
yields the positive solution c=100 for a (50,120,130) right triangle.
These should be the only solutions unless I'm missing something obvious.
Posted by Jer
on 2004-05-28 09:44:39