Answer
$(0, \frac{L \sqrt3}{6})$
Work Step by Step
We construct a coordinate system where the origin is located at the center of the base of the triangle. Finding the x center of mass is simple: since the object is symmetric, we can conclude that the center of mass must be at x=0. Next, we must find the y center of mass.
$ y_{cm} = \frac{my_1+my_2+my_3}{m+m+m}$
$ y_{cm} = \frac{m(0)+m(0)+m \frac{L \sqrt3}{2}}{m+m+m}$
$y_{cm}=\frac{L \sqrt3}{6}$
