#### Answer

Perimeter=$4\sqrt3+4\sqrt5$ inches
Area=$8+\sqrt{15}$ square inches

#### Work Step by Step

Perimeter is the sum of the lengths.
For a square, $P=4s$.
$P=4(\sqrt3+\sqrt5)$
Use the distributive property to simplify.
$P=4\sqrt3+4\sqrt5$
The area of a square is the product of the length of 2 sides.
$A=(\sqrt3+\sqrt5)(\sqrt3+\sqrt5)$
Use the FOIL method to multiply the two binomials.
$A=(\sqrt3\times\sqrt3)+(\sqrt3\times\sqrt5)+(\sqrt3\times\sqrt5)+(\sqrt5\times\sqrt5)$
Use the product rule for square roots to simplify.
$A=\sqrt9+\sqrt{15}+\sqrt{15}+\sqrt{25}$
Simplify square roots. Add like radicals.
$A=3+2\sqrt{15}+5=8+\sqrt{15}$