Difference between revisions of "2004 AIME I Problems/Problem 9"

 
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== Solution ==
 
== Solution ==
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{{solution}}
  
 
== See also ==
 
== See also ==
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* [[2004 AIME I Problems/Problem 8| Previous problem]]
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* [[2004 AIME I Problems/Problem 10| Next problem]]
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* [[2004 AIME I Problems]]
 
* [[2004 AIME I Problems]]

Revision as of 02:44, 6 November 2006

Problem

Let $ABC$ be a triangle with sides 3, 4, and 5, and $DEFG$ be a 6-by-7 rectangle. A segment is drawn to divide triangle $ABC$ into a triangle $U_1$ and a trapezoid $V_1$ and another segment is drawn to divide rectangle $DEFG$ into a triangle $U_2$ and a trapezoid $V_2$ such that $U_1$ is similar to $U_2$ and $V_1$ is similar to $V_2.$ The minimum value of the area of $U_1$ can be written in the form $m/n,$ where $m$ and $n$are relatively prime positive integers. Find $m+n.$

Solution

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See also