#### Answer

$(6\sqrt {2}+3\sqrt {5})$ inches

#### Work Step by Step

Finding the perimeter of the triangle involves adding the lengths of all its sides:
Perimeter=$\sqrt 8+\sqrt {32}+\sqrt {45}$
Perimeter=$\sqrt {2\times4}+\sqrt {2\times16}+\sqrt {9\times5}$
Perimeter=$2\sqrt {2}+4\sqrt {2}+3\sqrt {5}$
Perimeter=$(2+4)\sqrt {2}+3\sqrt {5}$
Perimeter=$(6\sqrt {2}+3\sqrt {5})$ inches