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:
- 7
- 6
- 6.4
- 5.5
The Correct Option is B
Approach Solution - 1
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:
\(EC = \frac{36}{6}\)
\(EC = 6\, \text{cm}\)
Approach Solution -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.
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