$$ EF=20cm $$

$$ \angle EDF=30^o $$

$$ \angle DEF=90^o $$

$$ Lengh\ of\ EG=? $$

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

$$ Lengh\ of\ ED=20\sqrt 3 $$

$$ \therefore Lengh\ of\ EG=\frac{20\sqrt 3}{2}=10\sqrt 3 $$