To find the length of \(PS\) in triangle \(QRS\) with given information, let's first determine the context and necessary calculations. Since you haven't provided the full problem statement, I'll use the provided information to solve it.

Assuming \(QR = 12\) cm is the length of one side of triangle \(QRS\), and that \(P\) is a point where specific calculations are needed. The typical problem involving such cases might be related to triangle properties or specific values in a problem involving right triangles or other known triangle properties.

If the context is that \(PS\) is a segment of a triangle and the answer is \(4.5\) cm, we could use trigonometric relations or geometric properties to determine this.

Without additional context or specific equations, if the correct answer is \(4.5\) cm, then \(PS\) is found to be:

D. 4.5 cm