2009 Gauss 8 Problem 24

Starting at point P, Breenah constructs a straight sided spiral so that:

- all angles are 90^\circ - after starting with a line segment of length 1, each side is 1 longer than the previous side.

After completing the side with length 21, Breenah's distance from her original starting point P will be between

\textbf{(A)}\ 13\ \text{and} 14\quad \textbf{(B)}\ 14\ \text{and} 15\quad \textbf{(C)}\ 15\ \text{and} 16\quad \textbf{(D)}\ 16\ \text{and} 17\quad \textbf{(E)}\ 17\ \text{and} 18

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.