Question 1210193
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Clearly the question that is asked is not the question that was SUPPOSED to be asked, because the length of CD is given.<br>
It is rather obvious, from the kind of information that is given, that the intended question was the length of AC.  In that case, the operative principle is that the angle bisector of an angle of  a triangle divides the opposite side into two segments whose lengths are in the same ratio as the lengths of the two sides of the triangle that include the given angle.<br>
Then, since the ratio of the lengths of BD and CD is 3:5 and side AB has length 6, side AC has length 10 by a simple proportion:<br>
{{{3:5=6:x}}}
{{{3x=30}}}
{{{x=10}}}<br>
ANSWER (to the intended question): 10<br>