Answer
($6\sqrt{2}+3\sqrt{5}$ ) meters
Work Step by Step
Adding all the sides of the triangle, the perimeter is
\begin{array}{l}\require{cancel}
\sqrt{8}+\sqrt{32}+\sqrt{45}
.\end{array}
Using the properties of radicals, the expression above simplifies to
\begin{array}{l}\require{cancel}
\sqrt{4\cdot2}+\sqrt{16\cdot2}+\sqrt{9\cdot5}
\\\\=
\sqrt{(2)^2\cdot2}+\sqrt{(4)^2\cdot2}+\sqrt{(3)^2\cdot5}
\\\\=
2\sqrt{2}+4\sqrt{2}+3\sqrt{5}
\\\\=
6\sqrt{2}+3\sqrt{5}
.\end{array}
