Answer
Perimeter $=18\sqrt {5}$ feet.
Area $=100$ square feet.
Work Step by Step
Length of the rectangle $l=\sqrt {125}$ feet.
Width of the rectangle $w=2\sqrt {20}$ feet.
Perimeter:
$\Rightarrow P=2l+2w$
Substitute values.
$\Rightarrow P=2(\sqrt {125})+2(2\sqrt {20})$.
Clear the parentheses.
$\Rightarrow P=2\sqrt {5^3}+4\sqrt {5\cdot 2^2}$.
Take the square root.
$\Rightarrow P=2\cdot 5\sqrt {5}+4\cdot 2\sqrt {5}$.
Simplify.
$\Rightarrow P=10\sqrt {5}+8\sqrt {5}$.
Use the distributive property.
$\Rightarrow P=(10+8)\sqrt {5}$.
Simplify.
$\Rightarrow P=18\sqrt {5}$.
Hence, the perimeter is $18\sqrt {5}$ feet.
Area :
$\Rightarrow A=lw$
Substitute values.
$\Rightarrow A=(\sqrt {125})(2\sqrt {20})$
Clear the parentheses.
$\Rightarrow A=2\sqrt {5^3}\cdot\sqrt {5\cdot2^2}$
Multiply the radicands and retain the common index.
$\Rightarrow A=2\sqrt {5^3\cdot5\cdot2^2}$
Simplify.
$\Rightarrow A=2\sqrt {5^4\cdot2^2}$
$\Rightarrow A=2\cdot 5^2\cdot2$
Simplify.
$\Rightarrow A=100$
Hence, the area is $100$ square feet.
