Difference between revisions of "2010 AMC 10A Problems/Problem 16"
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Revision as of 11:58, 4 July 2013
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.