the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. What are the possible values of x for this triangle?

Question

the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. What are the possible values of x for this triangle?

Answer 1

Let's say that you know two sides and say that their lengths are a, and b, and let x represent the unknown side's length. Then first of all, we have x<a+b.

Also we have a < x+b which means that x > a-b. Finally, b < x+a so x > b-a. This gives us x > Max(b-a,a-b) = |a-b|

Therefore we have our final result:

|a-b| < x < a+b

Answer 2

It sounds like there might be a diagram associated with this problem. If there is, maybe you could describe it. 

Answer 3

Hi, Austin.

Is there more to this question?

Kathye