Question 279110
Let the sides of the triangle be S.
The area of a triangle is 
{{{A=(1/2)BH}}}
In this case, 
{{{B=S}}}
Now we need to find H.
Draw it out.
The distance from the top vertex to the middle of the base is the height, H.
It forms a right triangle with one leg, H, the other leg, S/2, and the hypotenuse, S.
Use the Pythagorean theorem to find H in terms of S.
{{{S^2=H^2+(S/2)^2}}}
{{{H^2=S^2-(1/4)S^2}}}
{{{H^2=(3/4)S^2}}}
{{{H=(sqrt(3)/2)S}}}
Then from the area formula,
{{{A=(1/2)BH}}}
{{{A=(1/2)(S)(sqrt(3)/2)S}}}
{{{A=(sqrt(3)/4)S^2}}}
Then moving those terms around.
{{{S^2=4A/sqrt(3)}}}
{{{S=(2*sqrt(A))/(3^(1/4))}}}