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 |