AC=BC CD=BD=1/2 AC
CE垂直AD 得角GCB=角DAC
GB//AC 所以角GBC=角ACB=90
所以三角形GCB与三角形ADC全等
所以GB=CD
设AC=BC=2x
则GB=x AD=根号5 * x CE=2/根号5 x=2根号5/5 x
DE=根号(CD^2-CE^2 )=根号(x^2-4/5 x^2) =根号5 /5 x
所以Sgbc =1/2 GB*BC=1/2*x*2x=x^2
Scde=1/2 CE*DE=1/2*2根号5/5 x *根号5 /5 x =x^2/5
所以Sgbde=Sgbc-Scde=X^2-X^2/5=4X^2/5 =12
x=根号15
AE=AD-DE=根号5 x -根号5 /5 x =5根号3 -根号3=4根号3