Question 374582
Hmm. let's see: 
If x = unknown side, then the sides of the triangle are 4, 15, and x.  By a combination of the use of the triangle inequality,
4 + 15 > x, or 19 > x;
4+x > 15, or x > 11;
15 +x > 4, or x > -11.  This last inequality doesn't give us any new information.  But from the first two, we get
19 > x > 11. There are 7 possibilities, looking at your list.  Now you know...