∵ 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.