#### Answer

$1 \text{ }m$

#### Work Step by Step

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.