#### Answer

$13\sqrt{2}$

#### Work Step by Step

The diagonal and the two sides of the square form a right triangle with the legs equal to $13.$
Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $
a=13
$ and $
b=13
,$ then
\begin{array}{l}\require{cancel}
a^2+b^2=c^2
\\\\
13^2+13^2=c^2
\\\\
169+169=c^2
\\\\
c=\sqrt{169+169}
\\\\
c=\sqrt{169(2)}
\\\\
c=\sqrt{(13)^2\cdot2}
\\\\
c=13\sqrt{2}
.\end{array}
Hence, the missing side measures $
13\sqrt{2}
$ units.