Answer
$2\sqrt{131}
\text{ }
m
\text{ OR }
\approx 22.9
\text{ }
m$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Pythagorean Theorem to solve for the value of the missing side measurement.
$\bf{\text{Solution Details:}}$
Based on the given figure, the missing side is one of the legs of the right triangle. Let $a$ be the missing side measurement. Using the Pythagorean Theorem which is given by $a^2+b^2=c^2,$ with $b=
9
$ and $c=
11\sqrt{5}
,$ then
\begin{array}{l}\require{cancel}
a^2+9^2=(11\sqrt{5})^2
\\\\
a^2+81=121(5)
\\\\
a^2+81=605
\\\\
a^2=605-81
\\\\
a^2=524
.\end{array}
Taking the principal square root of both sides (since there are no negative side measurement) and simplifying the radical result to
\begin{array}{l}\require{cancel}
a=\sqrt{524}
\\\\
a=\sqrt{4\cdot131}
\\\\
a=\sqrt{(2)^2\cdot131}
\\\\
a=2\sqrt{131}
.\end{array}
Hence, the missing side is $
2\sqrt{131}
\text{ }
m
\text{ OR }
\approx 22.9
\text{ }
m
.$
