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 == | ||
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Revision as of 14:16, 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 |