or 32. the triangle could not be 5-12-13 because 24 does not divide into 5. for 8-15-17, if the short side is 3 times 8, then the long side would be 3 times 25, or 45.
moving on to the cases where the long side is 24 inches. candidates for the triangle are again 3-4-5, 5-12-13, and 8-15-17. for 3-4-5, if the long side is 6 times 4, then the short side is 6 times 3, or 18. for 5-12-13, if the long side is 2 times 12, then the short side is 2 times 5, or 10.
adding up all these values gives a final answer of 105.
a certain right triangle 