The cost of fencing an equilateral triangular park and a square park is the same. If the area of the triangular park is $$16\sqrt{3}m^{2}$$, the length of the diagonal of the square park is

Area of the equilateral triangle park is $$16\sqrt{\ 3}=\frac{\sqrt{\ 3}}{4}a^2$$   where "a" is the length of the side of the triangle

$$a^2=64\ or\ a=8\ cm$$ Now cost of fencing triangular and square park is same, hence their perimeter will also be same. Perimeter of the square park is 24cm

Hence the length of each side of square park is 6 cm. $$\sqrt{\ 6^2+6^2}=\sqrt{\ 72}=6\sqrt{\ 2}$$

Length of each diagonal is $$6\sqrt{\ 2}cm$$