In any triangle:
a/sina = b/sinb = c/sinc
Taking B, you have
a/sina = b/sin50 = c/sin50 (here since 2 internal angles are 50, abc is an isosceles triangle where b=c)
And you know angle 'a' = 180-100 = 80
a/sin80 = b/sin50
and you know a+2b = 16*root3
2 equations and 2 unknowns, you can solve for both a and b. Since b = c you can find the perimeter
Hope that helps