已知线段AB上有两点M,N,点M将AB分成2:3两部分,点N将AB分成4:1两部分,若MN=8cm,求AM,NB的长.

问题描述:

已知线段AB上有两点M,N,点M将AB分成2:3两部分,点N将AB分成4:1两部分,若MN=8cm,求AM,NB的长.

AM:MB=2:3
AM=2/5AB
AN:NB=4:1
NB=1/5AB
MN=AB-AM-NB
=AB-2/5AB-1/5AB
=2/5AB
AB=5/2MN
=5/2*8
=20
则AM=2/5AB=2/5*20=8
NB=1/5AB=1/5*20=4