12. What is the length of the line segment marked $x$ ?

A $\sqrt{2}$
B 2
C $2 \sqrt{2}$
D 3
E 4
12. D By Pythagoras' Theorem, $O B^{2}=O A^{2}+A B^{2}=1^{2}+1^{2}=1+1=2$. Similarly, $O C^{2}=O B^{2}+B C^{2}=2+1=3$ and $O D^{2}=O C^{2}+C D^{2}$ $=3+1=4$. Continuing in the same way, we see that $O E^{2}=5$, $O F^{2}=6, O G^{2}=7, O H^{2}=8, O I^{2}=9$.
So the length of the line segment marked $x$ is $\sqrt{9}=3$.