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Mathematics, 04.08.2019 01:40 Pookiev

The area of the smallest equilateral triangle with one vertex on each of the sides of the right triangle with side lengths and $2\sqrt{3},~5,$ 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. what is m + n + p?

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