Not-quite-diagonal

Geometry Level pending

With a rectangular sheet of paper, fold opposite corners to each other. The two creases should be the same length and bisect each other.

Given side lengths \(\frac {13}{3}\) and \(\frac {17}{7},\) if the "diagonal" has length \(\frac {a\sqrt{b}}{c}\), where \(a,b\) and \(c\) are positive integers with \(a,c\) coprime and \(b\) square-free. Find \(2a+c\).


I know, my paint skills are incredible.
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