Question 1073507
One side of the equilateral triangle, 2x.
Area,  {{{x^2*sqrt(3)}}}.
Area of the triangle given,  {{{8sqrt(3)=x^2*sqrt(3)}}}


{{{x=2sqrt(2)}}}


{{{2x=4sqrt(2)}}}, one whole side of the equilateral triangle.
Perimeter of both figures:  {{{12sqrt(2)}}}.



One side of the square of same perimeter is one quarter of that:
side of square,  {{{3sqrt(2)}}}.


Diagonal of the square:
{{{sqrt((9*2)^2+(9*2)^2)}}}
{{{sqrt(18+18)}}}
{{{sqrt(36)}}}
{{{highlight(diagonal=6)}}}