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Difference between revisions of "2011 AIME I Problems/Problem 8"
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In triangle <math>ABC</math>, <math>BC = 23</math>, <math>CA = 27</math>, and <math>AB = 30</math>. Points and are on with on , points  and  are on  with  on , and points  and  are on  with  on . In addition, the points are positioned so that , , and . Right angle folds are then made along , , and . The resulting figure is placed on a level floor to make a table with triangular legs. Let  be the maximum possible height of a table constructed from triangle  whose top is parallel to the floor. Then  can be written in the form , where  and  are relatively prime positive integers and  is a positive integer that is not divisible by the square of any prime. Find .
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In triangle <math>ABC</math>, <math>BC = 23</math>, <math>CA = 27</math>, and <math>AB = 30</math>. Points <math>V</math> and <math>W</math> are on <math>\overline{AC}</math> with <math>V</math> on <math> \overline{AW} </math>, points  and  are on  with  on , and points  and  are on  with  on . In addition, the points are positioned so that , , and . Right angle folds are then made along , , and . The resulting figure is placed on a level floor to make a table with triangular legs. Let  be the maximum possible height of a table constructed from triangle  whose top is parallel to the floor. Then  can be written in the form , where  and  are relatively prime positive integers and  is a positive integer that is not divisible by the square of any prime. Find .

Revision as of 00:07, 24 March 2011

In triangle $ABC$, $BC = 23$, $CA = 27$, and $AB = 30$. Points $V$ and $W$ are on $\overline{AC}$ with $V$ on $\overline{AW}$, points and are on with on , and points and are on with on . In addition, the points are positioned so that , , and . Right angle folds are then made along , , and . The resulting figure is placed on a level floor to make a table with triangular legs. Let be the maximum possible height of a table constructed from triangle whose top is parallel to the floor. Then can be written in the form , where and are relatively prime positive integers and is a positive integer that is not divisible by the square of any prime. Find .

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