Question

In triangle ABC, points D and E are on AB and AC, respectively, such that DE is parallel to BC. If AD = 6 cm, DB = 4 cm, and AE = 9 cm, then the length of EC (in cm) is:

• A. 7
• B. 6.4
• C. 6
• D. 5.5

Answer 1

Answer: (B)

6.4

Answer 2

Since DE is parallel to BC, triangles ADE and ABC are similar. Therefore, the ratios of corresponding sides are equal: $\frac{AD}{AB} = \frac{AE}{AC} \Rightarrow \frac{6}{6 + 4} = \frac{9}{9 + EC} \Rightarrow EC = 6.4$.