Difference between revisions of "2006 AIME II Problems/Problem 2"
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<cmath> 6.25 < n < 900 </cmath> | <cmath> 6.25 < n < 900 </cmath> | ||
− | 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>. | + | 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>\boxed{893}</math>. |
== See also == | == See also == |
Revision as of 00:45, 18 February 2019
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 • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.