Answer
$10\sqrt 2 ft \approx 14.1 ft$
Work Step by Step
Diagonal of a square room $20$ feet
Diagonal of a square is $\sqrt 2 a$ where $a$ is the side of the square.
$\sqrt 2 a = 20$
Squaring on both sides.
$(\sqrt 2 a)^{2} = 20 ^{2}$
$2 a^{2} = 400$
$ a^{2} = 200$
$a=\sqrt 200$
$a=\sqrt( 2 \times 100)$
$a=10\sqrt2 $
$a \approx 10 \times 1.414$
$a \approx 14.1$
Side of the square room $(a) = $ $10\sqrt2 $ ft.
or
Side of the square room $(a) $ $ \approx 14.1$ ft
