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

$1 \text{ }m$
Let the right triangle have $a$ and $b$ as the legs and $c$ as the hypotenuse. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $c=\sqrt{2}$ and $a=1 ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ 1^2+b^2=(\sqrt{2})^2 \\\\ 1+b^2=2 \\\\ b^2=2-1 \\\\ b^2=1 \\\\ b=\sqrt{1} \\\\ b=1 .\end{array} Hence, the other leg is $1 \text{ }m$ long.