Difference between revisions of "2006 AIME A Problems/Problem 2"
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<math> 6.25 < n < 900 </math> | <math> 6.25 < n < 900 </math> | ||
− | The number of possible integer values for <math>n</math> is the number of integers over the interval <math>(6.25 , 900)</math> which is <math> | + | The number of possible integer values for <math>n</math> is the number of integers over the interval <math>(6.25 , 900)</math> which is <math>893</math> |
== See also == | == See also == | ||
*[[2006 AIME II Problems]] | *[[2006 AIME II Problems]] |
Revision as of 10:41, 14 July 2006
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