State the formula

The area of an equilateral triangle with side length $a$ is given by the standard geometric formula.

$\text{Area} = \frac{\sqrt{3}}{4}a^2$

Substitute given values

Equate the formula to the given area value of $16\sqrt{3}$.

$\frac{\sqrt{3}}{4}a^2 = 16\sqrt{3}$

Solve for the side length $a$

Divide both sides by $\sqrt{3}$ and multiply by 4 to isolate $a^2$.

$a^2 = 16 \times 4 = 64$

Final calculation

Taking the square root of both sides gives the length of each side.

$a = \sqrt{64} = 8 \text{ cm}$