# Equilateral Triangle Dissection

**Geometry**Level 5

\(2\Delta xxx=\Delta aaa+\Delta bbb+\Delta ccc+3\Delta abc\)

where the notation \(\Delta abc\) shall denote the non-zero area of a triangle with sides \(a, b, c\), and \(x\) is the side of the equilateral triangle.

Find the minimum value \(a+b+c\) can have.