A parallelogram has adjacent sides of lengths $s$ units and $2s$ units forming a 45-degree angle. The area of the parallelogram is $8\sqrt 2$ square units. What is the value of $s$? Express your answer in simplest radical form.
If we let the side of length $2s$ be the base of the parallelogram, we can use our 45-degree angle to find the height of the parallelogram. The height and sides of the parallelogram form a 45-45-90 triangle, with the side of length $s$ as the hypotenuse. Thus, the height of the parallelogram is $s/\sqrt{2}$.

It follows that the area of the parallelogram is $2s\cdot (s/\sqrt{2}) = s^2\sqrt{2} = 8\sqrt{2}$, so $s^2 = 8$. Taking the square root of both sides, we see that $s = \boxed{2\sqrt{2}}$.