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23

Part of 1999 AMC 8

Problems(1)

1999 AMC 8 #23

Source:

6/17/2011
Square ABCDABCD has sides of length 3. Segments CMCM and CNCN divide the square's area into three equal parts. How long is segment CMCM ?
[asy] pair A,B,C,D,M,N; A = (0,0); B = (0,3); C = (3,3); D = (3,0); M = (0,1); N = (1,0); draw(A--B--C--D--cycle); draw(M--C--N); label("AA",A,SW); label("MM",M,W); label("BB",B,NW); label("CC",C,NE); label("DD",D,SE); label("NN",N,S);[/asy]
(A) 10(B) 12(C) 13(D) 14(E) 15 \text{(A)}\ \sqrt{10}\qquad\text{(B)}\ \sqrt{12}\qquad\text{(C)}\ \sqrt{13}\qquad\text{(D)}\ \sqrt{14}\qquad\text{(E)}\ \sqrt{15}
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