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题库 / OG2017Q-DS-184
In the quilting pattern shown above, a small square has its vertices on the sides of a larger square. What is the side length, in centimeters, of the larger square?
(1) The side length of the smaller square is 10 cm.
(2) Each vertex of the small square cuts 1 side of the larger square into 2 segments with lengths in the ratio of 1:2.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
题目分析：
（1） 已知小正方形的边长为DF=10cm，则~$DE^2+EF^2=DF^2=100$~，并不能得到CE的长
（2） 点D将CE切割为1:2的两段，即DE=2CD，又因为CD=EF，所以有DE=2EF。
因此，两个条件单独均不能解得CE长，综合两个条件，将条件2代入条件1，~$4EF^2+EF^2=5EF^2=100$~，解得EF=~$\sqrt{20}=2\sqrt{5}$~，又因为条件2得，DE=~$4\sqrt{5}$~，所以，大正方形边长CE=6~$\sqrt{5}$~。
综上所述，答案为（C），两个条件结合才能说明问题。