MathDB

Square

ABCD

has sides of length 3. Segments

CM

and

CN

divide the square's area into three equal parts. How long is segment

CM

?
[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("

A

",A,SW); label("

M

",M,W); label("

B

",B,NW); label("

C

",C,NE); label("

D

",D,SE); label("

N

",N,S);[/asy]

\text{(A)}\ \sqrt{10}\qquad\text{(B)}\ \sqrt{12}\qquad\text{(C)}\ \sqrt{13}\qquad\text{(D)}\ \sqrt{14}\qquad\text{(E)}\ \sqrt{15}

Problem Statement