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How many non-congruent right triangles are there, all of whose sides are poisitve integer lengths, and one of whsoe legs (i.e. not the hypotenuse) has length 12?

 Dec 30, 2022
 #1
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The answer is 10.

 Dec 30, 2022
 #2
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There are 4 right triangles as follows:

 

1 = (5, 13)
2 = (9, 15)
3 = (16, 20)
4 = (35, 37)

The 3rd side being 12 in each of above 4 triangles.

 Dec 31, 2022

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