Answer
$12 \sqrt{2}\; inches$.
Work Step by Step
Perimeter of the triangle is equal to the sum of all sides.
The sides of the given triangle is $\sqrt{32}\; in,\sqrt{50}\; in$ and $\sqrt{18}\; in$
Add all sides.
$=\sqrt{32}+\sqrt{50}+\sqrt{18}$
Factor radicands as a perfect square.
$=\sqrt{16\cdot 2}+\sqrt{25\cdot 2}+\sqrt{9\cdot 2}$
Use product rule.
$=\sqrt{16}\cdot \sqrt{2}+\sqrt{25}\cdot \sqrt{2}+\sqrt{9}\cdot \sqrt{2}$
Take square root of the perfect square.
$=4\cdot \sqrt{2}+5\cdot \sqrt{2}+3\cdot \sqrt{2}$
Factor out $\sqrt{2}$.
$=(4+5+3) \sqrt{2}$
Simplify.
$=12 \sqrt{2}$.
Hence, the perimeter is $12 \sqrt{2}\; inches$.
