In triangle ABC, segment DE is drawn parallel to side BC, with D on side AB and E on side AC. If AD = 4, DB = 6, and AC = 15, what is the…

Because $DE \parallel BC$, triangle $ADE$ is similar to triangle $ABC$, so corresponding sides are proportional: $\frac{AD}{AB} = \frac{AE}{AC}$. First, $AB = AD + DB = 4 + 6 = 10$. Then $\frac{4}{10} = \frac{AE}{15}$, so $AE = \frac{4 \times 15}{10} = 6$, choice A. Choice B (9) uses the ratio $\frac{DB}{AB} = \frac{6}{10}$, which gives $EC$, not $AE$. Choice C (10) is the length of $AB$. Choice D (11.25) comes from multiplying 15 by $\frac{3}{4}$, a ratio that does not appear in the figure. Use the part to the whole, $\frac{AD}{AB}$, not part to part.