Answer:
4 boxes of tiles.
Explanation:
Both rooms are square, so each has equal sides. Let's set a side to room A as x. It's area would be x^2. Room B has sides = 2x, so it's area would be (2x)^2 or 4x^2. The ratio of the areas B/A = 4x^2/x^2. B/A = 4.
Room B has 4 times the area of A. If one box of tile completes Room A, Room B would need four times that amount, or 4 boxes.