Question

如图,矩形纸片ABCD中,现将A、C重合,使纸片折叠压平,设折痕为EF.

Answer 1

连结AC,则EF是线段AC的垂直平分线,

AE=FC,设DF=x,

根据勾股定理,x^2+CD^2=FC^2,

CD=AB=4,

FC=8-x,

x^2+16=(8-x)^2,

x=3,

同理,设BE=x,

x^2+16=(8-x)^2,

x=3,

BE=3(cm),

作FH⊥BC,交BC于H,

FH=4,EH=BC-BE-FD=8-3-3=2,

EF^2=FH^2+EH^2=16+4=20,

EF=2√5（cm).