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A (non-degenerate) triangle with integer sides has perimeter 12. How many such non-congruent triangles are there?

 
Guest Aug 10, 2017
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Call a, b, c the sides

 

a + b + c  = 12  

 

And by the triangle inequality....

a + b > c

a + c > b

b + c > a

 

The greatest side can only  = 5   and the least side has to  be > 1

 

a    b     c

5    5     2

5    4     3

4    4     4

 

And these are the only possibilities

 

 

cool cool cool

 
CPhill  Aug 10, 2017

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