Answer:
- none if all sides are different lengths
- 7 if 2 or 3 sides can be the same length
Explanation:
If the side lengths are all different, none.
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The following 7 combinations will form triangles:
(5, 5, 5), (5, 5, 7), (5, 7, 7), (5, 15, 15)
(7, 7, 7), (7, 15, 15)
(15, 15, 15)
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Additional comment
The triangle inequality requires the sum of the two shortest lengths exceed the longest. Here, we have 5+7=12<15, so a triangle with all three lengths cannot be formed. We also note that 5+5=10<15, and 7+7=14<15, so isosceles triangles with only one side equal to 15 cannot be formed, either.