Consider the situation as shown in the figure. Locate the center of mass.

Explanation

Coordinates of `3m -= (L cos 60^(@) , L sin 60^(@))`
`-= ((L)/(2) ,(sqrt(3) L)/(2))`
`{:(,x,y),(m , 0 , 0),(2m , L,0),(3m , (L)/(2) ,(sqrt(3) L)/(2)):}`
`x_(c.m.) = ( m xx 0 + 2mL + 3m (L)/(2))/(m + 2m + 3m) = ((7mL)/(2))/(6m) = (7L)/(12)`
`y_(c.m.) = ( mxx 0 + 2m xx 0 + 3m xx (sqrt(3)L)/(2))/(m + 2m + 3m)`
`= ((3 sqrt(3) mL)/(2))/(6m) = (sqrt(3)L)/(4)`
`c.m-= ((7L)/(12), (sqrt(3) L)/(4))`
`c.m.-=((7L)/(12),(sqrt(3)L)/(4))`