Question

如图①,将边长为4cm的正方形纸片ABCD沿EF折叠(点E、F分别在边AB、CD上),使点B落在AD边上的点 M处,点C

Answer 1

(1)①因为EM=EB∴△AEM的周长=AB+AM=4+2=6_____cm；②作MG∥AE交EP于G,则EG=GPMG=(AE+DP)/2因为∠EMP=∠EBC=RT∠∴MG=EG=GP⇒EP=2MG∴EP=AE+DP(2)①设AE=K,在RT△AEM中,由勾股定理得：((4-K)^2)=(X^2)+(K^2)⇒K=(16-(X^2))/8∴EM=EB=4-[(16-(X^2))/8]=(16+(X^2))/8易知△AEM∼△DMP∴AE/MD=ME/MP则[(16-(X^2))/8]/(4-X)=[(16+(X^2))/8]/Y化简得Y=(16+(X^2))/(4+X)(0