如图,在△ABC中,DE∥FG∥BC,且AD:DF:FB=1:2:3,则S△ADE:S四边形DFGE:S四边形FBCG等
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/29 07:31:58
如图,在△ABC中,DE∥FG∥BC,且AD:DF:FB=1:2:3,则S△ADE:S四边形DFGE:S四边形FBCG等于( )
A. 1:9:36
B. 1:4:9
C. 1:8:27
D. 1:8:36
![](http://img.wesiedu.com/upload/7/42/742c653350c948392c079f44367baf5b.jpg)
B. 1:4:9
C. 1:8:27
D. 1:8:36
∵DE∥FG∥BC,
∴△ADE∽△AFG∽△ABC,
∵AD:DF:FB=1:2:3,
∴AD:AF:AB=1:3:6,
∴S△ADE:S△AFG:S△ABC=1:9:36,
设△ADE的面积是a,则△AFG和△ABC的面积分别是9a,36a,
则S四边形DFGE和S四边形FBCG分别是8a,27a,
∴S△ADE:S四边形DFGE:S四边形FBCG等=1:8:27.
故本题选C.
∴△ADE∽△AFG∽△ABC,
∵AD:DF:FB=1:2:3,
∴AD:AF:AB=1:3:6,
∴S△ADE:S△AFG:S△ABC=1:9:36,
设△ADE的面积是a,则△AFG和△ABC的面积分别是9a,36a,
则S四边形DFGE和S四边形FBCG分别是8a,27a,
∴S△ADE:S四边形DFGE:S四边形FBCG等=1:8:27.
故本题选C.
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