# Constrained Triangle

Geometry Level 5

We have three parallel lines $$l, m$$ and $$n$$ and an equilateral triangle $$CDE$$ with its vertices on these lines as shown in figure.

The distance between the lines $$l$$ and $$m$$ is 5 and between $$m$$ and $$n$$ is 2.

The side length of triangle can be expressed as $$A \sqrt{B}$$, where $$A$$ and $$B$$ are positive integers with $$B$$ square-free. Find $$A + B$$.

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