An important property of an isoceles triangle is that the perpendicular drawn from the vertex between equal sides to the unequal side divides the angle at the vertex into two.

Let the isoceles triangle be ABC, with Angle A being 120 degrees and Angle B= Angle C=30 degrees
Now we draw a perpendicular from vertex A to side BC at point D, resulting in 2 right angle triangles ADB and ADC
Hence the Angle A will be split into two parts of 60 degrees each when we draw a perpendicular.

Applying some basic trigonometry in the resulting triangle ADB
cos30=$\frac{\sqrt{3}}{2}$=$\frac{6\sqrt{3}}{AB}$
Hence side AB=12

Similarly side AC=12

Perimeter= AB+BC+AC= $24+12\sqrt{3}$