ABC中,AB=4,D,E,F分别在AB,AC,BC上,DE平行于BC,EF平行于AB,那么AD=时,四边形BFED的面积是原1/4

Question

ABC中,AB=4,D,E,F分别在AB,AC,BC上,DE平行于BC,EF平行于AB,那么AD=___时,四边形BFED的面积是原1/4

Answer 1

设S△ABC=a
∵SღDEFB=a/4 DE//BC,EF//AC EF=AD=AB/n=4/n
又S△CEF:S△ABC= ﹙EF/AB﹚ ² =1/n² S△AED:S△ABC=﹙AD/AB﹚²=1/n²
S△CEF =S△ABC/n²=a/ n² S△AED=S△ABC/n² =a//n²
∴SღDEFB=a－2a/n² =a/4
n² =8/3
n=2√6/3=1.633
AD=4/1.633=2.45
∴AD=2.45_时,四边形BFED的面积是原△ABC面积的1/4.