Answer
Perimeter $=24\sqrt {5}$ feet.
Area $=160$ square feet.
Work Step by Step
Length of the rectangle $l=4\sqrt {20}$ feet.
Width of the rectangle $w=\sqrt {80}$ feet.
Perimeter:
$\Rightarrow P=2l+2w$
Substitute values.
$\Rightarrow P=2(4\sqrt {20})+2(\sqrt {80})$.
Clear the parentheses.
$\Rightarrow P=8\sqrt {5\cdot2^2}+2\sqrt {5\cdot 2^4}$.
Take the square root.
$\Rightarrow P=8\cdot 2\sqrt {5}+2\cdot 4\sqrt {5}$.
Simplify.
$\Rightarrow P=16\sqrt {5}+8\sqrt {5}$.
Use the distributive property.
$\Rightarrow P=(16+8)\sqrt {5}$.
Simplify.
$\Rightarrow P=24\sqrt {5}$.
Hence, the perimeter is $24\sqrt {5}$ feet.
Area :
$\Rightarrow A=lw$
Substitute values.
$\Rightarrow A=(4\sqrt {20})(\sqrt {80})$
Clear the parentheses.
$\Rightarrow A=4\sqrt {5\cdot2^2}\cdot\sqrt {5\cdot2^4}$
Multiply the radicands and retain the common index.
$\Rightarrow A=4\sqrt {5\cdot2^2\cdot5\cdot2^4}$
Simplify.
$\Rightarrow A=4\sqrt {5^2\cdot2^6}$
$\Rightarrow A=4\cdot 5\cdot2^3$
Simplify.
$\Rightarrow A=160$
Hence, the area is $160$ square feet.
