What Do They Have In Common?

Let us denote the length of the side of the Equilateral Triangle by $a$ .
Therefore,
Area of the equilateral triangle $= \frac{\sqrt 3}{4} a^2$
Perimeter of the equilateral triangle $= 3a$

Equating the two gives us,
$\frac{\sqrt 3}{4} a^2 = 3a$
$\Rightarrow a = 4\sqrt 3$
Therefore, length of each side of the given equilateral triangle is $4 \sqrt 3$ .

Using this value to find the numerical value, we get Perimeter $P = 3a \Rightarrow P = 3 \times 4\sqrt 3 \Rightarrow \boxed{P = 12\sqrt 3}$ .