Solution: according to the meaning of the question, angle ABD= angle BDA= angle DAB=60 degrees, AB=AD=BD=2, so angle DAC=30 degrees; Because: angle BDC= 180 degrees, so angle ADC= 120 degrees, so angle ACD=30 degrees, DC=2, so BC = BD+DC = 4；; Take AE midpoint as E point, D point as DE vertical AC, and E as vertical foot and AC midpoint; So the angle ADE=60 degrees; Because triangle ADE= triangle EDC is a right triangle and AD=2, DE= 1, AE=EC root number 3, so AC=AE+EC= double root number 3; Therefore, the perimeter of the triangle ABC =AB+AC+BC=2+4+ double root number 3=6+ double root number 3.