Question

点D、E在线段AB上且都在AB中点的同侧,点D分AB为2：5两部分,点E分AB为4：5两部分,若DE=5cm,求AB的长

Answer 1

不妨设点D、E都在靠近A点的一侧；（不论靠近哪一侧,结果是相同的）

则有：AD：DB = 2：5 ,AE：EB = 4：5 ,

可得：AD/AB = AD/(AD+DB) = 2/(2+5) = 2/7 ,AE/AB = AE/(AE+EB) = 4/(4+5) = 4/9 ；

则有：AD = (2/7)AB ,AE = (4/9)AB ,

所以,DE = AE-AD = (4/9-2/7)AB = (10/63)AB ,

可得：AB = (63/10)DE = 31.5 cm .