Question

3 connecting lines are shown. Line A B is horizontal. Line A C is about half the length of A B. Line B C is about one-third of the length of A B.
Which inequality can be used to explain why these three segments cannot be used to construct a triangle?

AC + AB > CB
AC + CB < AB
AC + CB > AB
AC + AB < CB

Answer 1

AC + CB < AB

Reason: triangle inequality requires the sum of any two sides to be greater than the third. Here AC ≈ 1/2 AB and CB ≈ 1/3 AB, so AC + CB ≈ (1/2 + 1/3)AB = (5/6)AB < AB, so the inequality fails.