Problem E

Fold Once

A rectangular piece of paper, \(PQRS\), has \(PQ = 30\) cm and \(PS = 40\) cm. The paper has grey lines on one side and is plain white on the other.

The paper is folded so that the two diagonally opposite corners \(P\) and \(R\) coincide. This creates a crease along line segment \(AC\), with \(A\) on \(PS\) and \(C\) on \(QR\).

Determine the length of \(AC\).