Difference between revisions of "2006 AIME I Problems/Problem 8"
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== Problem == | == Problem == | ||
Hexagon <math> ABCDEF </math> is divided into four rhombuses, <math> \mathcal{P, Q, R, S,} </math> and <math> \mathcal{T,} </math> as shown. Rhombuses <math> \mathcal{P, Q, R,} </math> and <math> \mathcal{S} </math> are congruent, and each has area <math> \sqrt{2006}. </math> Let <math> K </math> be the area of rhombus <math> \mathcal{T}. </math> Given that <math> K </math> is a positive integer, find the number of possible values for <math> K. </math> | Hexagon <math> ABCDEF </math> is divided into four rhombuses, <math> \mathcal{P, Q, R, S,} </math> and <math> \mathcal{T,} </math> as shown. Rhombuses <math> \mathcal{P, Q, R,} </math> and <math> \mathcal{S} </math> are congruent, and each has area <math> \sqrt{2006}. </math> Let <math> K </math> be the area of rhombus <math> \mathcal{T}. </math> Given that <math> K </math> is a positive integer, find the number of possible values for <math> K. </math> | ||
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== Solution == | == Solution == | ||
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== See also == | == See also == | ||
Revision as of 01:09, 6 November 2006
Problem
Hexagon 
is divided into four rhombuses, 
and 
as shown. Rhombuses 
and 
are congruent, and each has area 
Let 
be the area of rhombus 
Given that is a positive integer, find the number of possible values for 
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Solution
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