Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set - Page 631: 42

$c=25 \text{ } m$

Using $a^2+b^2=c^2$ or the Pythagorean Theorem, then, \begin{array}{l}\require{cancel} 7^2+24^2=c^2 \\\\ 49+576=c^2 \\\\ 625=c^2 \\\\ c=\pm\sqrt{625} \\\\ c=\pm\sqrt{(25)^2} \\\\ c=\pm25 .\end{array} Since there are no negative measurements, then $ c=25 \text{ } m .$