Mathematics > Standard Multiple Choice

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

In triangle A B C, the length of side  is 2 and the length of side  is 12. Which of the following could be the length of side ?

(A) 6

(B) 8

(C) 10

(D) 12

(E) 14

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The correct answer is D

Explanation

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