A rectangular sheet ABCD has AB = 8 cm and BC = 6 cm. It is folded so that corner C lands exactly on corner A. How long is the crease?

The crease is the part of the perpendicular bisector of AC inside the sheet. With A(0, 0) and C(8, 6), the bisector through (4, 3) meets the long sides at (6.25, 0) and (1.75, 6). Its length is $\sqrt{4.5^2+6^2}=7.5$ cm.