Question

4,7 and a are the measure of sides of a triangle. Find the range of values of a.

Answer 1

Using the triangle inequality theorem for the above triangle:
s+4 > 7 $⟹$ s > 3
s+7 > 3 $⟹$ s > -3 (not valid because length of sides must be positive)
7+4 > s $⟹$ s < 11

combining the two valid statements:
3 < s < 11