Problem:
How many non-congruent triangles with perimeter have integer side lengths?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The longest side cannot be greater than , since otherwise the remaining two sides would not be long enough to form a triangle. The only possible triangles have side lengths or .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions