△ABC中,∠ADE=∠C,AD=DB,AC=3AE,若BC=6,则DE=

问题描述:

△ABC中,∠ADE=∠C,AD=DB,AC=3AE,若BC=6,则DE=

ABC相似于AED
AB/AE=BC/DE=AC/AD
2AD/AE=6/DE=3AE/AD
(AD/AE)^2=3/2
AD/AE=√(3/2)=(√6)/2
DE=6/[(√6)/2]=2√6