Answer
$2\sqrt{10} \text{ } m.$
Work Step by Step
Using $a^2+b^2=c^2$ (or the Pythagorean Theorem) where a leg is given the measure $3$ meters and the hypotenuse is given the measure $7$ meters, then the other leg, $b$, is equal to
\begin{array}{l}\require{cancel}
3^2+b^2=7^2
\\\\
b^2=7^2-3^2
\\\\
b^2=49-9
\\\\
b^2=40
\\\\
b=\sqrt{40}
\\\\
b=\sqrt{4\cdot10}
\\\\
b=\sqrt{(2)^2\cdot10}
\\\\
b=2\sqrt{10}
.\end{array}
Hence, the unknown side is $
$
