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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

In triangle ABC, the length of side line BC is 2 and the length of side line AC is 12. Which of the following could be the length of side line AB?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14

答案和解析

答案：D

解析：

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, B C + A B greater than A C, or 2 + A B greater than 12. Thus, A B greater than 10, which eliminates options (A), (B), and (C). Also by the Triangle Inequality, B C + A C greater than A B, or 14 greater than A B, which eliminates choice (E). Therefore, of the given choices, only choice (D), 12, could be the length of side line AB.