∵ Quadrilateral ABCD is a rectangle,

∴AB=CD=15cm, ∠A=∠D=90°, AD∥BC, AD=BC,

∴∠DEC=∠A′CB,

According to the properties of folding, we get: A′B=AB=15cm, ∠BA′E=∠A=90°,

∴A′B=CD, ∠BA′C=∠D=90°,

In △A′BC and △DCE,

∠BA′C=∠D∠ A′CB＝∠DECA′B＝CD,

∴△A′BC≌△DCE (AAS),

∴A′C=DE,

Suppose A′C=xcm, then BC=AD=DE+AE=x+9 (cm),

In Rt△A′BC, BC2=A′B2+A′C2,< /p>

That is (x+9)2=x2+152,

The solution is: x=8,

∴A′C=8cm.

So the answer is: 8.