Find the number of non-congruent right triangles, where all the sides are positive integers, and one of the legs is $6$.

Guest Aug 29, 2023

#1**+1 **

*Find the number of non-congruent right triangles, where all the sides are positive integers, and one of the legs is $6$.*

It's talking about right triangles, therefore c^{2} = a^{2} + b^{2}

The problem requires that all sides be integers, i.e., no fractions.

There's only **one** triangle that I can find to satisfy both conditions. That's 6, 8, 10.

BTW, a right triangle with integer sides is called a Pythagorean Triple.

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Bosco Aug 29, 2023

#2**+1 **

There have been a lot of repeated questions lately. I put together a proof to determine why the 6-8-10 right triangle is the only one that exists, as Bosco discovered, in case you want more details: https://web2.0calc.com/questions/help-right-triangles#r2

The3Mathketeers Aug 30, 2023