如图,三角形ABC,DE平行于BC,S三角形ABC=9/2S三角形DCE则S三角形ADE:S三角形ABC=

设S△ABC=9a,则S△DEC=2a,S△ADE=xa
∵DE//BC
∴△AED∽△ABC
AE/AC=AD/AB
AE/CE=AD/BD
S△ADE/S△DEC=S△ADC/S△BDC
ax/2a=(ax+2a)/(9a-2a-xa)
消去a,化简得x²-5x+4=0
x1=1,x2=4
S△AED：△ABC=1:9或4:9