Question

question 5 of 5
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a triangle has two sides with lengths of 8 and 17. complete the compound inequality to expresses the possible values for the lengths of the third side, x.

Explanation:

Step1: Apply triangle - side - length inequality (difference)

The difference of the two given side lengths gives a lower - bound. If two sides of a triangle have lengths \(a = 17\) and \(b = 8\), then \(|a - b|\lt x\).
\(|17 - 8|=9\), so \(9\lt x\).

Step2: Apply triangle - side - length inequality (sum)

The sum of the two given side lengths gives an upper - bound. \(x\lt a + b\).
Since \(a = 17\) and \(b = 8\), \(a + b=17 + 8 = 25\), so \(x\lt25\).

Answer:

\(9\lt x\lt25\)