Difference between revisions of "2010 AMC 12A Problems/Problem 14"
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Revision as of 17:02, 11 February 2010
Problem
Nondegenerate has integer side lengths, is an angle bisector, , and . What is the smallest possible value of the perimeter?
Solution
By the Angle Bisector Theorem, we know that . If we use the lowest possible integer values for AB and BC (the measures of AD and DC, respectively), then , contradicting the Triangle Inequality. If we use the next lowest values ( and ), the Triangle Inequality is satisfied. Therefore, our answer is , or choice .