Question

if two sides of a triangle are 6 and 16,what is the range of the possible lengths for the third side.

Answer 1

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

- x + 6 > 16 ⇒ x > 10
- x + 16 > 6 ⇒ x > -10 (redundant)
- 6 + 16 > x ⇒ x < 22

So 10 < x < 22. (If degenerate "triangle" with zero area is allowed, x = 10 or x = 22.)