Let side a = 5. Let side b = 9. Then the triangle has
sides
a=5, b=9, and c=?. Any side of a triangle must be less
than the other two sides added together, so
a < b+c, b < a+c, and c < a+b
Substituting:
5 < 9+c, 9 < 5+c, and c < 5+9
Solving all three for c:
-4 < c, 4 < c, c < 14
The first one is of course true, so ignore it.
Put the second and third together and get
4 < c < 14
