smc

Draw perpendicular lines from their if goe[ radii of the circles to the sides of the triangle, and lines from the radii of the circles to the vertices of the triangle. Because the triangle is equilateral, the lines divide the big triangle into a small triangle, three rectangles, and six small $30-60-90$ triangles. The Longer length of the rectangles is 6 because it is the radius of one circle + the radius of another ($3+3$). The length of one side is $2(3\sqrt{3})+6=6\sqrt{3}+6$. The perimeter is $\boxed{18+18\sqrt{3}}$.