Question

a triangle has two sides of length 19 and 6. what compound inequality describes the possible lengths for the third side, x? write a compound inequality like 1 < x < 3.

Explanation:

Step1: Apply triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So \(x + 6>19\) and \(x+19 > 6\) (the second one is always true for positive - valued \(x\)) and \(19 + 6>x\).
From \(x + 6>19\), we get \(x>19 - 6\), so \(x>13\).
From \(19 + 6>x\), we get \(x<25\).

Answer:

\(13