The Official SAT Question of the Day™

In triangle ABC, the length of side BC is 2 and the length of side AC is 12. Which of the following could be the length of side AB?

A. 6
B. 8
C. 10
D. 12
E. 14
Correct Answer: D

Here's Why:
By the Triangle Inequality, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Therefore, BC + AB > AC, or 2 + AB > 12. Thus, AB > 10, which eliminates options (A), (B), and (C). Also by the Triangle Inequality, BC + AC > AB, or 14 > AB, which eliminates choice (E). Therefore, of the given choices, only choice (D), 12, could be the length of side.

Difficulty: Medium
Question Type: Standard Multiple Choice

(Mathematics)