If the length of each median of an equilateral triangle is $6 \sqrt{3}$ cm, the perimeter of the triangle is

If AB = x cm, then

$\mathrm{BD}=\frac{x}{2} \mathrm{~cm}$

$\therefore$ From $\triangle \mathrm{ABD}$

AB² = BD² + AD²

$\Rightarrow x^{2}=\frac{x^{2}}{4}+(6 \sqrt{3})^{2}$

$\Rightarrow x^{2}-\frac{x^{2}}{4}=36 \times 3$

$\Rightarrow \frac{3 x^{2}}{4}=36 \times 3$

$\Rightarrow x^{2}=36 \times 4$

$\Rightarrow x=6 \times 2=12 \mathrm{~cm}$

∴ Perimeter of equilateral triangle = 3 × 12

= 36 cm