Find the number of non-congruent right triangles, where all the sides are positive integers, and one of the legs is $6$.
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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 c2 = a2 + b2
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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+177 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
