In the triangle above, DC is parallel to AB. What is the len

In the triangle above, DC is parallel to AB. What is the length of DC?

(1) AB = 14
(2) EC = CB

Please, confirm whether my solution is correct. If we consider both statements, we can notice that triangles AEB and DEC are the "same" triangle, except for the size. In other words, both have the same angles. Therefore, the relationship between any of two of their sides must be the same. Then,

\frac{14}{EB} = \frac{DC}{EC}

But we know that EC = 0.5*EB

Then: DC = 7

My answer is the OA.

Is it valid what I have done? I remember that I learned this in high school :s.Image may be NSFW.
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