Difference between revisions of "2019 AMC 12B Problems/Problem 9"
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==Problem== | ==Problem== | ||
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| + | For how many integral values of <math>x</math> can a triangle of positive area be formed having side lengths <math>\log_{2} x, \log_{4} x, 3</math>? | ||
==Solution== | ==Solution== | ||
Revision as of 15:49, 14 February 2019
Problem
For how many integral values of 
can a triangle of positive area be formed having side lengths 
?
Solution
The lower bound for x would be x=4, where the sides of the triangle would be (2,1,3). The upper bound for x would be x=4, where the sides of the triangle would be (6,3,3). The number of integers strictly between 4 and 64 is 64 - 4 - 1 = 59
-DrJoyo
See Also
| 2019 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 8 |
Followed by Problem 10 |
| 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 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
