Constrained Triangle

Geometry Level 5

We have three parallel lines l,ml, m and nn and an equilateral triangle CDECDE with its vertices on these lines as shown in figure.

The distance between the lines ll and mm is 5 and between m m and nn is 2.

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

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