To sum up, there are two ways of looking at the problem:
1. In similar figures the ratio of two sides in one is the same as the ratio of the corresponding sides in the other.
PS:7=9:4 or PS/7 = 9/4
2. If two figures are similar, one of them may be viewed as an enlargement of the other, so that the ratio of corresponding sides will be the same.
PS:9 = 7:4 or PS/9 = 7/4
Another way of saying this is that everything in the larger rectangle is 7/4 or 1.75 as large as the corresponding side in the smaller rectangle. That is to say that the scaling factor is 1.75.
What is nice about this viewpoint is that if you had two similar figures with many sides of different lengths, you could get from one to the other by multiplying or dividing the length by the scaling factor. Additionally, if you knew the area of one you could get the area of the other by multiplying or dividing by the square of the scaling factor.