Answer
The perimeter of the triangle is closest to 18.
Work Step by Step
Take the sum of all the sides.
$\sqrt {30}+\sqrt {10}+\sqrt {90}$
Approximate the values of the square roots based on the closest perfect square.
ex. $\sqrt {30}\approx5.4$ because the nearest perfect squares are $\sqrt {25}$ and $\sqrt {36}$ (between 5 and 6)
Repeat this approximation with the other square roots.
$5.4+3.1+9.5\approx18$
Common mistake (this is illegal math):
$\sqrt {30}+\sqrt {90}+\sqrt {10}=\sqrt{130}$
$\sqrt {130}\approx12$ (wrong)
because
$\sqrt {30}+\sqrt {90}+\sqrt {10}\ne\sqrt {30+90+10}$
