Question

ahab wants to draw a triangle with side lengths of 19 centimeters and 20 centimeters. what is the range of possible lengths for the third side that he can use? write your answer as a compound inequality using x.

Explanation:

Step1: Apply triangle inequality theorem

Let the third side be \(x\). According to the triangle inequality theorem, the sum of two sides of a triangle must be greater than the third side. So \(x + 19>20\) (which simplifies to \(x>20 - 19\) or \(x > 1\)) and \(x+20>19\) (always true for positive \(x\)) and \(19 + 20>x\) (or \(x<39\)).

Answer:

\(1