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Find the number of ordered triples of integers (a, b, c) that form the side lengths of a triangle with positive area and perimeter 20.

 Feb 9, 2020
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First: list all the possible lengths of the sides:

   2,9,9     3,8,9     4,8,8     4,7,9     5,6,9     5,7,8     6,6,8     6,7,7

 

and then, find all the ways that these lengths can be written:

as:  for  2,9,9  they can be interchanged as:  2,9,9     9,2,9     9,9,2

and for  5,7,8  they can be interchanged as:  5,7,8     5,8,7     7,5,8     7,8,5     8,5,7     8,7,5

 Feb 9, 2020

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