矩形$\mathit{ABCD}$中，$\mathit{AB}=6$，$\mathit{BC}=8$．点$P$在矩形$\mathit{ABCD}$的内部，点$E$在边$\mathit{BC}$上，满足$\mathit{\Delta PBE}\backsim \mathit{\Delta DBC}$，若$\mathit{\Delta APD}$是等腰三角形，则$\mathit{PE}$的长为　　．