Answer
Perimeter P $ = 24 \sqrt 5 $ feet
Area A = 160 Square feet
Work Step by Step
$ P = 2l + 2w $
Substitute $ l = 4\sqrt 20 $ and $w = \sqrt80 $
$P = 2 \times 4\sqrt 20 + 2 \times \sqrt 80$
$ = 8\sqrt 20 + 2 \sqrt 80$
Split $\sqrt 20$ and $\sqrt 80$ into two factors such that one is a perfect square.
$ = 8 \sqrt (4 \times 5) + 2 \sqrt (16 \times 5)$
$= 8 \sqrt 4 \sqrt 5 + 2 \sqrt 16 \sqrt 5$
$= 8 \times 2 \times \sqrt 5 + 2 \times 4 \times \sqrt 5$
$ = 16\sqrt 5 + 8 \sqrt 5$
$ = 24\sqrt 5$
P $ = 24\sqrt 5$ feet
Area = $l \times w$
$= 4\sqrt 20 \times \sqrt 80$
$= 4 \sqrt (4 \times 5) \times \sqrt (16 \times 5)$
$ = 4 \times\sqrt 4 \times\sqrt 5 \times\sqrt 16 \times\sqrt 5$
$ = 4 \times 2 \times \sqrt 5 \times 4 \times \sqrt 5 $
$ = 32 \times \sqrt 5 \times \sqrt 5 $
$ = 32 \times 5 $
Area = 160 Square feet
