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, and the difference between the lengths of any two sides must be less than the length of the third side. Let the lengths of the other two sides be \(XY = a\) and \(YZ=b\). Then \(|a - b|\lt XZ\lt a + b\). Since no side - lengths are given, assume for simplicity that \(XY = 3\) and \(YZ = 4\).

Step2: Find a possible side - length

If \(XY = 3\) and \(YZ = 4\), then \(|4 - 3|=1\) and \(4 + 3 = 7\). A possible value for \(XZ\) could be \(5\) (since \(1\lt5\lt7\)).

Step3: Find an impossible side - length

An impossible value for \(XZ\) could be \(8\) because \(8>4 + 3\), violating the triangle - inequality theorem.

Answer:

a. 5
b. 8