If two sides of a triangle are of measures 15 and 28, what is the range of possible values for the third side x?

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