$$EF=20cm$$

$$\mathrm{\angle }EDF={30}^o$$

$$\mathrm{\angle }DEF={90}^o$$

$$LenghofEG=?$$

As EF=20cm so by applying the ratios of triangles having angles 30, 60 and 90 degrees, we can see that

$$LenghofED=20\sqrt{3}$$

$$\therefore LenghofEG=\frac{20\sqrt{3}}{2}=10\sqrt{3}$$