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
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.