Question

the measure of two sides of a triangle are 7 and 11. determine the range of values for the third side of the triangle

Answer 1

Let the third side be x. By the triangle inequalities:

- x + 7 > 11 ⇒ x > 4
- x + 11 > 7 ⇒ x > −4 (automatic)
- 7 + 11 > x ⇒ x < 18

So x must satisfy 4 < x < 18. (If integer lengths are required, x can be 5,6,...,17. x = 4 or 18 gives a degenerate straight-line triangle.)