Difference between revisions of "2002 AIME I Problems/Problem 15"
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== Problem == | == Problem == | ||
| + | Polyhedron <math>ABCDEFG</math> has six faces. Face <math>ABCD</math> is a square with <math>AB = 12;</math> face <math>ABFG</math> is a trapezoid with <math>\overline{AB}</math> parallel to <math>\overline{GF},</math> <math>BF = AG = 8,</math> and <math>GF = 6;</math> and face <math>CDE</math> has <math>CE = DE = 14.</math> The other three faces are <math>ADEG, BCEF,</math> and <math>EFG.</math> The distance from <math>E</math> to face <math>ABCD</math> is 12. Given that <math>EG^2 = p - q\sqrt {r},</math> where <math>p, q,</math> and <math>r</math> are positive integers and <math>r</math> is not divisible by the square of any prime, find <math>p + q + r.</math> | ||
== Solution == | == Solution == | ||
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== See also == | == See also == | ||
| − | + | {{AIME box|year=2002|n=I|num-b=14|after=Last Question}} | |
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Revision as of 15:16, 25 November 2007
Problem
Polyhedron 
has six faces. Face 
is a square with 
face 
is a trapezoid with 
parallel to 
and 
and face 
has 
The other three faces are 
and 
The distance from 
to face is 12. Given that 
where 
and 
are positive integers and is not divisible by the square of any prime, find 
Solution
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See also
| 2002 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
