2006 AIME II Problems/Problem 2
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Problem
The lengths of the sides of a triangle with positive area are 
, 
, and 
, where 
is a positive integer. Find the number of possible values for .
Solution
By the Triangle Inequality:
Also:
Combining these two inequalities:
The number of possible integer values for is the number of integers over the interval 
, which is 
.
See also
| 2006 AIME II (Problems • Resources) | ||
| Preceded by Problem 1 | Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
