2015 AMC 12A Problems/Problem 2: Difference between revisions
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==Problem== | |||
Two of the three sides of a triangle are 20 and 15. Which of the following numbers is not a possible perimeter of the triangle? | Two of the three sides of a triangle are 20 and 15. Which of the following numbers is not a possible perimeter of the triangle? | ||
<math> \textbf{(A)}\ 52\qquad\textbf{(B)}\ 57\qquad\textbf{(C)}\ 62\qquad\textbf{(D)}}\ 67\qquad\textbf{(E)}\ 72</math> | |||
==Solution== | |||
The third side must be less than 20 + 15 = 35 by the Triangle Inequality, and so the perimeter must be less than 20 + 15 + 35 = 70. Clearly, <math>\boxed{E}</math> must be our answer. | |||
Revision as of 18:06, 4 February 2015
Problem
Two of the three sides of a triangle are 20 and 15. Which of the following numbers is not a possible perimeter of the triangle?
$\textbf{(A)}\ 52\qquad\textbf{(B)}\ 57\qquad\textbf{(C)}\ 62\qquad\textbf{(D)}}\ 67\qquad\textbf{(E)}\ 72$ (Error compiling LaTeX. Unknown error_msg)
Solution
The third side must be less than 20 + 15 = 35 by the Triangle Inequality, and so the perimeter must be less than 20 + 15 + 35 = 70. Clearly, 
must be our answer.
