1981 AHSME Problems/Problem 25

Problem 25 In $\triangle ABC$ in the adjoining figure, $AD$ and $AE$ trisect $\angle BAC$ . The lengths of $BD$ , $DE$ and $EC$ are $2$ , $3$ , and $6$ , respectively. The length of the shortest side of $\triangle ABC$ is

[asy] defaultpen(linewidth(.8pt)); pair A = (0,11); pair B = (2,0); pair D = (4,0); pair E = (7,0); pair C = (13,0); label(" $A$ ",A,N); label(" $B$ ",B,SW); label(" $C$ ",C,SE); label(" $D$ ",D,S); label(" $E$ ",E,S); label(" $2$ ",midpoint(B--D),N); label(" $3$ ",midpoint(D--E),NW); label(" $6$ ",midpoint(E--C),NW); draw(A--B--C--cycle); draw(A--D); draw(A--E); [/asy] $\textbf{(A)}\ 2\sqrt{10}\qquad \textbf{(B)}\ 11\qquad \textbf{(C)}\ 6\sqrt{6}\qquad \textbf{(D)}\ 6\qquad \textbf{(E)}\ \text{not uniquely determined by the given information}$

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1981 AHSME Problems/Problem 25