如图1,点c,d在线段AB上,且都在AB中点的同侧,点C分AB为3比7两部分,点D分AB为2比3两部分,若CD=2,求AB的长

Question

如图1,点c,d在线段AB上,且都在AB中点的同侧,点C分AB为3比7两部分,点D分AB为2比3两
部分,若CD=2,求AB的长

Answer 1

设AB长为k
C分AB长为3:7
则AC ：CB = 3 :7
AC长为3/(3+7)*AB = 3/10 * AB
D分AB为2:3
则AD :DB = 2:3
则AD长为2/(2+3)*AB = 2/5*AB
那么
CD = AD - AC = (2/5 - 3/10)*AB = 1/10*AB = 2
则
AB = 20