△ABC,AB,AC,BC长为12,18,24厘米,在AB和AC上分别取E和F点使△AEF的周长为30厘米?

问题描述:

△ABC,AB,AC,BC长为12,18,24厘米,在AB和AC上分别取E和F点
使△AEF的周长为30厘米?

令AE/AC=AF/AB于是有
△ABC与△AFE相似
有AE/AC=AF/AB=EF/BC
由和分比定理得
AE/AC=AF/AB=(AE+AF+EF)/(AB+BC+AC)=30/58
于是得到了AE=270/29
AF=180/29