Question

determine the range of possible side lengths of the third side \\( \overline { a b } \\) of \\( a b c \\) from least to greatest. \\( 2 < x < 18 \\) \\( 0 < x < 8 \\) \\( 0 \leq x \leq 18 \\) \\( 2 \leq x \leq 18 \\)

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for a triangle with sides \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Here \(a = 10\), \(b = 8\), and \(c=x\).
First, calculate \(|10 - 8|\):
\(|10 - 8|=2\)
Then, calculate \(10 + 8\):
\(10+8 = 18\)

Answer:

\(2\lt x\lt18\)