Question

here is triangle xyz. a. list one possible side length for xz. b. list one impossible side length for xz:

Explanation:

Step1: Recall 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. Let the lengths of the other two sides be \(a\) and \(b\), and the side we want to find be \(c\). Then \(|a - b|\lt c\lt a + b\).

Step2: Assume side lengths for illustration

Suppose the lengths of the other two - sides of \(\triangle XYZ\) are \(3\) and \(5\). Then \(|5 - 3|\lt xz\lt5 + 3\), so \(2\lt xz\lt8\).

Step3: Find a possible side - length

A possible side - length for \(xz\) could be \(4\) (since \(2\lt4\lt8\)).

Step4: Find an impossible side - length

An impossible side - length for \(xz\) could be \(10\) (since \(10\gt8\)).

Answer:

a. 4
b. 10