Explanation:
we would have needed only one corresponding side length. because for similar triangles all corresponding lines (like sides but also heights and so on) would be related in size by using the same scaling factor.
going from the large to the small triangle : what do I need to multiply the large side length with to get the small one ?
27 × x = 9
x = 9/27 = 1/3
that is the scale factor.