Question

here is triangle abc.
a. list one possible length for side ac.
b. list one impossible length for ac.

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 \(AB = 12\), \(BC=16\), and \(AC = x\). Then \(|AB - BC|\lt x\lt AB + BC\).

Step2: Calculate the range of \(AC\)

We have \(|12 - 16|=4\) and \(12 + 16 = 28\). So \(4\lt x\lt28\).

Answer:

a. 10 (any value between 4 and 28 exclusive is correct)
b. 3 (any value less than or equal to 4 or greater than or equal to 28 is correct)