Difference between revisions of "2010 AMC 10A Problems/Problem 16"
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Revision as of 13:55, 2 April 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 
.
See also
| 2010 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 15 |
Followed by Problem 17 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
