Answer
The length of each piece is $4$ inches.
Work Step by Step
Set up the equation:
$A = A_s + A_l$
$2 = (\frac{x}{4})^2+(\frac{8-x}{4})^2$
Simplify the equation
$2 = \frac{x^2}{4^2}+\frac{(8-x)^2}{4^2}$
$2 = \frac{x^2}{16}+\frac{64-16x+x^2}{16}$
Multiply both sides by $16$. Thus, the equation becomes:
$32=x^2+64-16x+x^2$
$0=2x^2-16x+32$
Divide both sides by $2$
$0=x^2-8x+16$
Factor.
$0=(x-4)(x-4)$
$0=(x-4)$
$x=4$
The length of each piece is equal to their perimeters.
$P_{square1}=4(\frac{x}{4})$
$P_{square1}=4(\frac{4}{4})$
$P_{square1}=4$ $inches$
$P_{square2}=4(\frac{8-x}{4})$
$P_{square2}=4(\frac{8-4}{4})$
$P_{square2}=4(\frac{4}{4})$
$P_{square2}=4$ $inches$