Answer
Perimeter = 18 $\sqrt 5$ feet
Area = 100 Square Feet
Work Step by Step
$ P = 2l + 2w $
Substitute $ l = \sqrt 125 $ and $w = 2\sqrt 20 $
$P = 2 \sqrt 125 + 2 ( 2\sqrt 20)$
$ = 2 \sqrt 125 + 4\sqrt 20$
Split $ \sqrt 125 $ and $\sqrt 20$ into two factors such that one is a perfect square.
$ = 2 \sqrt( 25 \times 5) + 4 \sqrt( 4 \times 5) $
$ = 2 \sqrt 25 \times \sqrt 5 + 4 \sqrt 4 \times \sqrt 5 $
$ = 2 \times 5 \times \sqrt 5 + 4 \times 2 \times \sqrt 5 $
$ = 10\sqrt 5 + 8 \sqrt 5 $ Apply Distributive Property
$= (10 + 8) \sqrt 5$
$P = 18 \sqrt 5$ feet
Area A $ = l \times w$
$ = \sqrt 125 \times 2 \sqrt 20$
$=\sqrt (25 \times 5) \times 2 \sqrt (4 \times 5)$
$=\sqrt 25 \times \sqrt 5 \times 2\times \sqrt 4\times \sqrt 5$
$= 5 \times \sqrt 5 \times 2 \times 2 \times \sqrt 5$
$= 20 \sqrt5 \sqrt 5$
$= 20 \times 5$
Area A$ = 100 $ Square feet
