In triangle $ABC$, medians $\overline{AD}$ and $\overline{BE}$ are perpendicular.  If $AC = 22$ and $BC = 31$, then find $AB$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
In triangle $ABC$, medians $\overline{AD}$ and $\overline{BE}$ are perpendicular.  If $AC = 22$ and $BC = 31$, then find $AB$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
17
In triangle $ABC$, medians $\overline{AD}$ and $\overline{BE}$ are perpendicular.  If $AC = 22$ and $BC = 31$, then find $AB$.
train