olymmath

HMMT 2013 U17

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The lines y=x,y=2xy=x, y=2 x, and y=3xy=3 x are the three medians of a triangle with perimeter 1. Find the length of the longest side of the triangle.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{\sqrt{58}}{2+\sqrt{34}+\sqrt{58}}

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