Chapter 10 - Exponents and Radicals - 10.7 The Distance Formula, the Midpoint Formula, and Other Applications - 10.7 Exercise Set - Page 676: 10

$c=10\sqrt{2} \\\\ c\approx14.142 $

In the given right triangle, $a$ and $b$ are the legs and $c$ is the hypotenuse. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $ a=10 $ and $ b=10 ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ 10^2+10^2=c^2 \\\\ 100+100=c^2 \\\\ 200=c^2 \\\\ c=\sqrt{200} \\\\ c=\sqrt{100\cdot2} \\\\ c=\sqrt{(10)^2\cdot2} \\\\ c=10\sqrt{2} \\\\ c\approx14.142 .\end{array}