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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 $6$.

 Aug 29, 2023
 #1
avatar+901 
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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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 Aug 29, 2023
 #2
avatar+177 
+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

 Aug 30, 2023

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