Length of a line

Geometry Level 3

In the figure above \(ABCD\) is a square and \(AFB\) is a right \(\triangle\). What is the length of \(FE\) ? If your answer is of the form \(x\sqrt{y}\) where \(x\) and \(y\) are coprime positive integers, give your answer as \(x+y\).

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