108 yards. The ratio of the sides for Square A to Square B is 4:9 with Square A's side as 12 yards. Therefore, substituting 4x and 9x for the respective sides of Squares A and B, you can solve Square A for x=3 and multiply 3 times 9 to get 27 for the side of Square B. Then, since the perimeter is the sum of all sides, and a square has equal sides, you can multiply 27 (as the side of Square B) and 4 (the number of sides in a square) to get a perimeter of 108 yards for Square B.