2006 AIME II Problems/Problem 2
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 and applying the well-known logarithmic property , we have that
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 • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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