Could someone explain, I have no idea.

Actually, there are only 8 triangles.

How many non-congruent triangles with perimeter 16 inches are there whose side lengths are all integer numbers of inches?

I got 5

2,7,7

3,6,7

4,5,7

4,6,6,

5,5,6

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2+6+7=15 so that it no good

In fact all yours have a perimater of 15, but the question says the perimeter is 16.