If x is the side length of the equilateral triangle, the height (perpendicular bisector of a side) is √x²-¼x²=x√3/2.
The area of a triangle is ½base×height=(x/2)(x√3/2)=x²√3/4. So x²√3/4=55, x²=220/√3=127.02 approx. Therefore x, the side length=√127.02=11.27 approx.