如图所示已知△ABC的面积S=1在图1中若AA1/AB=BB1/BC=CC1/CA=1/2如图,已知的△ABC面积S△ABC=1.1、若AA1/AB=BB1/BC=CC1/CA=1/2,则S△A1B1C1=1/4；2、若AA2/AB=BB2/BC=CC2/CA=1/3,则S△A2B2C2=1/3；3、若AA3/AB=BB3/BC=CC3/CA=1/4,则

Question

如图所示已知△ABC的面积S=1在图1中若AA1/AB=BB1/BC=CC1/CA=1/2
如图,已知的△ABC面积S△ABC=1.
1、若AA1/AB=BB1/BC=CC1/CA=1/2,则S△A1B1C1=1/4；
2、若AA2/AB=BB2/BC=CC2/CA=1/3,则S△A2B2C2=1/3；
3、若AA3/AB=BB3/BC=CC3/CA=1/4,则S△A3B3C3=7/16；
按此规律,若AA8/AB=BB8/BC=CC8/CA=1/9,则S△A8B8C8=

Answer 1

S△ABC=1/1=1/1^2,
S△A1B1C1=1/4=1/2^2,
S△A2B2C2=1/3=3/9=(1*2+1)/3^2,
S△A3B3C3=7/16=(2*3+1)/4^2,
依此类推
S△A8B8C8=（7*8+1）/9^2=57/81