如图,在梯形ABCD中,AD∥BC,AD=3,BC=9,AB=6,CD=4,若EF∥BC,且梯形AEFD与梯形EBCF的周长相等,则EF的长为(  ) A.457 B.335 C.395 D.152

问题描述:

如图,在梯形ABCD中,AD∥BC,AD=3,BC=9,AB=6,CD=4,若EF∥BC,且梯形AEFD与梯形EBCF的周长相等,则EF的长为(  )
A.

45
7

B.
33
5

C.
39
5

D.
15
2

由已知AD+AE+EF+FD=EF+EB+BC+CF,∴AD+AE+FD=EB+BC+CF=12(AD+AB+BC+CD)=11∵EF∥BC,∴EF∥AD,AEEB=DFFC设AEEB=DFFC=k,AE=kk+1AB=6kk+1,DF=kk+1CD=4kk+1AD+AE+FD=3+6kk+1+4kk+1=13k+3k+1∴13k+3k+1=11...