如图,在△ABC中,AB=14cm,AD/BD=5/9,DE∥BC,CD⊥AB,CD=12cm.求△ADE的周长.

问题描述:

如图,在△ABC中,AB=14cm,

AD
BD
5
9
,DE∥BC,CD⊥AB,CD=12cm.求△ADE的周长.

∵AB=14cm,ADBD=59∴ADAB=514∴AD=5cm,BD=9cm又∵CD⊥AB∴CB2=BD2+CD2=92+122=225∴CB=15cm∵AC2=AD2+CD2=52+122=169∴AC=13cm∴△ABC的周长为42cm又∵DE∥BC,∴△ADE∽△ABCC△ADEC△ABC=ADAB=514∴△ADE的周长...