smc

Let the radius of the circle be $r$. Let $s_1$ be the side length of the square inscribed in the semicircle and $s_2$ be the side length of the square inscribed in the entire circle. For the square in the semicircle, we have $s_1^2+(\frac{s_1}{2}{)}^2=r^2\Rightarrow s_1^2=\frac{4}{5}{r}^2$. For the square in the circle, we have $s_2\sqrt{2}=2r\Rightarrow s_2^2=2r^2$. Therefore, $s_1^2:s_2^2=\frac{4}{5}{r}^2:2r^2=\boxed{2:5}$