Difference between revisions of "2000 AMC 10 Problems/Problem 10"
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Revision as of 16:05, 3 March 2024
Problem
The sides of a triangle with positive area have lengths 
, 
, and 
. The sides of a second triangle with positive area have lengths , , and 
. What is the smallest positive number that is not a possible value of 
?
Solution
Since and are fixed sides, the smallest possible side has to be larger than 
and the largest possible side has to be smaller than 
. This gives us the triangle inequality 
and 
. 
can be attained by letting 
and 
. However, 
cannot be attained. Thus, the answer is 
.
See Also
| 2000 AMC 10 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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. 
