Triangles with perimeter 7

[brightmind]

How many non-congruent triangles with perimeter 7 have interger side lengths?
My answer is 5 , since we can construct the following triangles: 1-1-5, 1-2-4, 1-3-3, 2-2-3.
But the answer is only 2. The triangles are 1-3-3, 2-2-3. They say that the longest side could not be greater than 3, since otherwise the remaining two sides wouldn't be long enough to form a triangle .
Can some one explain for me? I think 1-1-5 is a reasonable solution.

 

[mmm4444bot]

… we can construct the following triangles: 1-1-5, 1-2-4, …

How did you construct these two triangles?

I don't see how, since:

5 > 1 + 1

4 > 1 + 2

:?

 

[Denis]

... I think 1-1-5 is a reasonable solution.

C'mon brightmind...take a stick 5 inches long and 2 sticks each 1 inch long: can you construct a triangle?

 

[brightmind]

yeah.. i see. thanks