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.
+23246 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
