# Tricky Triangle

Geometry Level 4

$$X$$ , $$Y$$ and $$Z$$ are 3 mutually parallel straight lines in a plane, such that $$Y$$ is between $$X$$ and $$Z$$ and the distance between $$X$$ and $$Y$$ is $$10$$ units and the distance between $$Y$$ and $$Z$$ is $$6$$ units. $$ABC$$ is an equilateral triangle with $$A$$ on $$X$$ , $$B$$ on $$Y$$ and $$C$$ on $$Z$$. If the area of $$\triangle ABC$$ can be expressed as $$\dfrac{a^2}{\sqrt{b}}$$ where $$a$$ and $$b$$ are coprime positive integers and $$b$$ is not divisible by the square of any prime, find the value of $$a+b$$.

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