When a shape's area is 9 times as great, the one dimension difference is √9=3 times as great. Therefore the length of all sides are 3 times of the corresponding sides of the original shape. The shortest side in the original shape is 3, the larger one is 3 times of that, which is 9.
General rule, if a similar shape is x times ratio in terms of sides, the area will be x^2 times the original.