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:
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:
Updated On: Oct 28, 2024
- 7
- 6.4
- 6
- 5.5
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The Correct Option is B
Solution and Explanation
Since DE is parallel to BC, triangles ADE and ABC are similar. Therefore, the ratios of corresponding sides are equal: $\frac{AD}{AB} = \frac{AE}{AC} \Rightarrow \frac{6}{6 + 4} = \frac{9}{9 + EC} \Rightarrow EC = 6.4$.
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