2006 iTest Problems/Problem 27
Revision as of 12:54, 7 December 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 27 -- Tilted Triangle)
Problem
Line passes through and into the interior of the equilateral triangle . and are the orthogonal projections of and onto respectively. If and , then the area of can be expressed as , where and are positive integers and is not divisible by the square of any prime. Determine .
Solution
Let be the intercept of and . By the Vertical Angle Theorem, . Also, since both and are perpendicular to , . Thus, by AA Similarity. Since , and .
Let be the side length of the triangle, so . By the Pythagorean Theorem, . Also, , so by the Law of Cosines, .
By using the Pythagorean Theorem again, we have Thus, the area of the triangle is , so .
See Also
2006 iTest (Problems, Answer Key) | ||
Preceded by: Problem 26 |
Followed by: Problem 28 | |
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