Difference between revisions of "2003 AIME II Problems/Problem 14"
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== Problem == | == Problem == | ||
| + | Let <math>A = (0,0)</math> and <math>B = (b,2)</math> be points on the coordinate plane. Let <math>ABCDEF</math> be a convex equilateral hexagon such that <math>\angle FAB = 120^\circ,</math> <math>\overline{AB}\parallel \overline{DE},</math> <math>\overline{BC}\parallel \overline{EF,}</math> <math>\overline{CD}\parallel \overline{FA},</math> and the y-coordinates of its vertices are distinct elements of the set <math>\{0,2,4,6,8,10\}.</math> The area of the hexagon can be written in the form <math>m\sqrt {n},</math> where <math>m</math> and <math>n</math> are positive integers and n is not divisible by the square of any prime. Find <math>m + n.</math> | ||
== Solution == | == Solution == | ||
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== See also == | == See also == | ||
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Revision as of 14:41, 21 November 2007
Problem
Let 
and 
be points on the coordinate plane. Let 
be a convex equilateral hexagon such that 
and the y-coordinates of its vertices are distinct elements of the set 
The area of the hexagon can be written in the form 
where 
and 
are positive integers and n is not divisible by the square of any prime. Find 
Solution
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See also
| 2003 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
