## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$13\sqrt{2}$
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.