Simone如图，将矩形$ABCD$的四个角向内折起，恰好拼成一个无缝隙无重叠的长方形$EFGH$，若$EH=9$厘米，$EF=12$厘米，则边$AD$的长是______厘米.
的有关信息介绍如下：
$\because $四边形$EFGH$为矩形.$\therefore HG$∥$EF$，$\therefore \angle GHF=\angle EFH$，又$\because \angle BFE=\angle EFH$，$\angle DHG=\angle GHF$，$\therefore \angle EFB=\angle DHG$，在$\triangle DHG$和$\triangle BEF$中$\left\{\begin{array}{l}{∠B=∠D}\\{∠BFE=∠DHG}\\{EF=HG}\end{array}\right.$，$\therefore \triangle DHG$≌$\triangle BEF\left(AAS\right)$，$\therefore HD=EF$，$\therefore MF=HD$，$\therefore AD=AH+HD=HM+MF=HF$，$\because \angle HEM=\angle AEH$，$\angle BEF=\angle FEM$，$\therefore \angle HEF=\angle HEM+\angle FEM=\frac{1}{2}\times 180^{\circ}=90^{\circ}$，$\therefore HF=\sqrt{E{H}^{2}+E{F}^{2}}=\sqrt{{9}^{2}+1{2}^{2}}=15(厘米)$，$\therefore AD=15(厘米)$，故答案为：$15$.
