Question

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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 the triangle - inequality theorem (difference of two sides)

The difference of the lengths of two sides of a triangle is less than the length of the third side. So, \(|17 - 8|\lt x\). Since \(17-8 = 9\), we have \(9\lt x\).

Step2: Apply the triangle - inequality theorem (sum of two sides)

The sum of the lengths of two sides of a triangle is greater than the length of the third side. So, \(x\lt17 + 8\). Since \(17+8=25\), we have \(x\lt25\).

Answer:

\(9\lt x\lt25\)