# Problem of the Week 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 $$AC$$.