As shown in figure 1，point C is on the segment BG and quadrilateral ABCD is a square. ????

Question

As shown in figure 1，point C is on the segment BG and quadrilateral ABCD is a square. AG intersects BD and CD at points E and F, respectively. If AE=5 and EF=3, then FG=( )
如图1所示，C点在线段BG上，四边形ABCD是一个正方形。AG分别与BD相交于E点，与CD相交于F点。如果AE=5 EF=3, 那么 FG=( )?
图片可能不清楚，谢谢了！

Answer 1

FG=16/3
设正方形边长为a，CG长度为b，FG长度为x
a/(a+b)=5/(3+x)
b/a=x/8
解得x=16/3
就是运用相似三角形的知识，ADF相似于CFG，ADE相似于BEG，虽然有三个未知数，但是会自然消掉一个。

Answer 2

AD:DF=5:3
DC:DF=5:3
DF:FC=3:2=AF:FG=8:FG
FG=2*8/3=16/3

Answer 3

AD:DF=5:3
DC:DF=5:3
DF:FC=3:2=AF:FG=8:FG
FG=2*8/3=16/3

Answer 4

aaa