In triangle ABC, the angle A is twice the size of angle B, and angle C is the smallest angle. The sides opposite angles A, B, and C are of lengths 10, $x$, and $y$, respectively. If the perimeter of triangle ABC is given as 30 units, what is the length of side $x$?
Use the fact that the sum of angles in a triangle is $180^{ ext{o}}$ to find the angles, and apply the Law of Sines for finding the missing side.