2013 AIME I Problems/Problem 9: Difference between revisions
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==Problem 9== | ==Problem 9== | ||
A paper equilateral triangle <math>ABC</math> has side length 12. The paper triangle is folded so that vertex <math>A</math> touches a point on side <math>\overline{BC}</math> a distance 9 from point <math>B</math>. The length of the line segment along which the triangle is folded can be written as <math>\frac{m\sqrt{p}}{n}</math>, where <math>m</math>, <math>n</math>, and <math>p</math> are positive integers, <math>m</math> and <math>n</math> are relatively prime, and <math>p</math> is not divisible by the square of any prime. Find <math>m+n+p</math>. | A paper equilateral triangle <math>ABC</math> has side length 12. The paper triangle is folded so that vertex <math>A</math> touches a point on side <math>\overline{BC}</math> a distance 9 from point <math>B</math>. The length of the line segment along which the triangle is folded can be written as <math>\frac{m\sqrt{p}}{n}</math>, where <math>m</math>, <math>n</math>, and <math>p</math> are positive integers, <math>m</math> and <math>n</math> are relatively prime, and <math>p</math> is not divisible by the square of any prime. Find <math>m+n+p</math>. | ||
== Solution == | |||
<math>\boxed{113}</math> | |||
== See also == | |||
{{AIME box|year=2013|n=I|num-b=8|num-a=10}} | |||
Revision as of 20:45, 16 March 2013
Problem 9
A paper equilateral triangle 
has side length 12. The paper triangle is folded so that vertex 
touches a point on side 
a distance 9 from point 
. The length of the line segment along which the triangle is folded can be written as 
, where 
, 
, and 
are positive integers, and are relatively prime, and is not divisible by the square of any prime. Find 
.
Solution
See also
| 2013 AIME I (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 | ||
| All AIME Problems and Solutions | ||
