如图,AB∥EF∥CD,已知AB=20,CD=80,BC=100,那么EF的值是(  ) A.10 B.12 C.16 D.18

问题描述:

如图,AB∥EF∥CD,已知AB=20,CD=80,BC=100,那么EF的值是(  )
A. 10
B. 12
C. 16
D. 18

∵AB∥CD,
∴△EAB∽△ECD,

BE
ED
=
AB
CD

而AB=20,CD=80,
BE
ED
=
20
80
=
1
4

BE
BD
=
1
5

又∵EF∥CD,
EF
CD
=
BE
BD
=
1
5

而CD=80,
∴EF=
80
5
=16.
故选C.