Question 429889
Solution:Let x cm the side of equilateral triangle, then half of its perimeter will be: 3x/2 cm. If we apply Heron's Formula of triangle area, we have:

{{{A=sqrt((p-a)*(p-b)*(p-c))}}}, where p is half of perimeter and a=b=c=x cm the 

sides of triangle.Substitute the given of our problem:

{{{12sqrt(3)=sqrt(((3x/2)-x))^3}}}, squaring both sides,

{{{432=((3x/2)-x)^3}}}

{{{432=x^3/8}}},

x^3=432(8) => x=cubic root((432)(8)) => x=12(cubic root(2))cm

Done.