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2017 AIME I Problems/Problem 15

Revision as of 17:54, 8 March 2017 by Math129 (talk | contribs) (Created page with "The area of the smallest equilateral triangle with one vertex on each of the sides of the right triangle with side lengths <math>2\sqrt{3},~5,</math> and <math>\sqrt{37},</mat...")
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The area of the smallest equilateral triangle with one vertex on each of the sides of the right triangle with side lengths $2\sqrt{3},~5,$ and $\sqrt{37},$ as shown, is $\frac{m\sqrt{p}}{n},$ where $m,~n,$ and $p$ are positive integers, $m$ and $n$ are relatively prime, and $p$ is not divisible by the square of any prime. Find $m+n+p.$

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