Question 429889
Solution:Apply Heron's Formula for equilateral triangle with side x xm have:

{{{A=sqrt((3x/2)*(3x/2-x)^3)}}}, substituting our data we have:

{{{12*sqrt(3)=sqrt((3x/2)*(x^3/8))}}}, squaring both sides we have:

{{{432=3x^4/16}}}

{{{6912=3x^4}}}, divide by 3

{{{2304=x^4}}}, => x=fourth root of 2304 =>. Approximately x=7 cm.

Answer: The side of equilateral triangle with area 20.78 cm^2 is 6.93 cm.

Done.