#### Answer

The dimensions of the square is $3 \times 3$ inches.
The dimensions of the rectangle is $6 \times 3$ inches.

#### Work Step by Step

Let $a = $ area of the rectangle
Let $x = $ area of the square
Let $p = $ width of rectangle and length of square
$a = 2x$
$2x = 2p^{2}$
$a = 6 \times p$
$a = 2p^{2}$
$6p = 2p^{2}$
$6p - 2p^{2}= 0$
$2p(3 - p) = 0$
$p = 0, 3$
Recall, 0 is not a valid value for length.
Therefore, the dimensions of the square are $3 \times 3$ inches.
Therefore, the dimensions of the rectangle are $6 \times 3$ inches.