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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