Question

如图,矩形ABCD中,E,F分别在BC,AD上,矩形ABCD～矩形ECDF,AB=2,S矩形ABCD=9S矩形ECDF,

Answer 1

答案=12

求解如下：

答：因为：S矩形ABCD=9S矩形ECDF

所以：AB*BC = 9*EC*CD , 又因为：AB = CD =2

所以：BC = 9 EC (1)

因为：矩形ABCD～矩形ECDF

所以：AB/EC = BC/CD

将（1）代入并整理

9 EC*EC =4,EC =2/3, BC = 9*EC =6

S矩形ABCD = AB *BC = 2*6 =12

S矩形ECDF = EC*CD = 2/3*2 = 4/3

解答完毕