Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set - Page 631: 46

$a=12 \text{ } cm$

Using $a^2+b^2=c^2$ or the Pythagorean Theorem, then, \begin{array}{l}\require{cancel} a^2+5^2=13^2 \\\\ a^2+25=169 \\\\ a^2=169-25 \\\\ a^2=144 \\\\ a=\pm\sqrt{144} \\\\ a=\pm\sqrt{(12)^2} \\\\ a=\pm12 .\end{array} Since there are no negative measurements, then $ a=12 \text{ } cm .$