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
• C. 6.4
• D. 5.5

Answer 1

The Correct Option is B

In triangle ABC, DE is parallel to BC. 

AD = 6 cm, DB = 4 cm, AE = 9 cm. We need to find EC.

By the Basic Proportionality Theorem (Thales' Theorem), \(\frac{AD}{DB} = \frac{AE}{EC}\).

\(\frac{6}{4} = \frac{9}{EC}\)

\(EC = \frac{9 \times 4}{6} = \frac{36}{6} = 6\) cm.