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

To find the length of EC, we use the Basic Proportionality Theorem (also known as Thales' theorem), which states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Given that DE is parallel to BC, we apply the theorem to find:

\(\frac{AD}{DB} = \frac{AE}{EC}\)

We have:

\(AD = 6\, \text{cm}, \quad DB = 4\, \text{cm}, \quad AE = 9\, \text{cm}\)

Substitute the known values into the equation:

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

Cross-multiplying gives:

\(6 \times EC = 9 \times 4\)

\(6 \times EC = 36\)

Solving for EC, we divide both sides by 6:

\(EC = \frac{36}{6}\)

\(EC = 6\, \text{cm}\)

Answer 2

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.