For questions regarding enlargements of shapes, it's sometimes easier to consider one dimension at a time. So for this example, let's first consider what the area of the rectangle would be if we just enlarged the length by a scale factor of 3. We can do this by multiplying the area by 3:
20cm^2 * 3 = 60cm^2
Now, let's consider enlarging the width of this rectangle by a scale factor of 3:
60cm^2 * 3 = 180cm^2
Notice that we end up multiplying the area of the rectangle by 3^2. The 3 is the scale factor that we're asked to enlarge by, and the 2 is the number of dimensions that we are enlarging the shape in.