# Just be quick with calculations

Geometry Level 3

$$ABC$$ is an equilateral triangle such that vertices $$B,C$$ lie on two parallel lines at a distance of 6 units. If $$A$$ lies between the parallel lines at a distance 4 units from one of them, then the length of the side of the triangle is of the form

$$\large{A\sqrt{\frac{B}{C}}}$$, where $$A,B,C$$ are co prime natural numbers.

Find $$A+B+C$$.

×