So for this, we will be applying the Triangle Inequality Theorem, which states that the sum of 2 sides must be greater than the third side for it to be a triangle. If any inequality turns out to be false, then the set cannot be a triangle.
Let A = 6, B = 10, and C = 12:
Let A = 5, B = 7, and C = 10
Let A = 4, B = 4, and C = 9
Let A = 2, B = 3, and C = 3
Since the third option had an inequality that was false, <u>the third option cannot be a triangle.</u>