如图,梯形ABCD中,AD∥BC,点E在BC上,AE=BE,点F是CD的中点,且AF⊥AB,若AD=2.7,AF=4,AB=6,则CE的长为(  ) A.22 B.23−1 C.2.5 D.2.3

问题描述:

如图,梯形ABCD中,AD∥BC,点E在BC上,AE=BE,点F是CD的中点,且AF⊥AB,若AD=2.7,AF=4,AB=6,则CE的长为(  )
A. 2

2

B. 2
3
−1
C. 2.5
D. 2.3

延长AF、BC交于点G.∵AD∥BC,∴∠D=∠FCG,∠DAF=∠G.又DF=CF,∴△AFD≌△GFC.∴AG=2AF=8,CG=AD=2.7.∵AF⊥AB,AB=6,∴BG=10.∴BC=BG-CG=7.3.∵AE=BE,∴∠BAE=∠B.∴∠EAG=∠AGE.∴AE=GE.∴BE=12BG=5...