Question 975748
Let us say that both polygons have n sides. 
Length of each side of polygon#1 = {{{x[1]}}}       
Hence, perimeter[1] = {{{n*x[1]}}}
Length of each side of polygon#2 = {{{x[2]}}}    
Hence, perimeter[2] = {{{n*x[2] = 27}}}
 
We know already, {{{x[1]/x[2]}=2/3}}}

{{{(Perimeter[1]/Perimeter[2]) = n*x[1]/n*x[2]}}}
            {{{Perimeter[1]/27 = x[1]/x[2]}}}
               {{{Perimeter[1] = (2/3) * 27}}}
               {{{Perimeter[1] = 18}}}

Therefore, perimeter of smaller polygon is 18.