# Triangle Inside Parabola

Geometry Level 3

An equilateral triangle is inscribed in the parabola $$x^2=8y$$ such that one of its vertices is at the vertex of this parabola.

The side length of the triangle can be written as $$q\sqrt{p}$$ ; where $$q$$ and $$p$$ are natural numbers and $$p$$ is a prime. Find $$p+q$$.

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