Geometry

Triangles

Medium

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, $AE = 9$ cm, then the length of $EC$ (in cm) is:

6.4

5.5

✅ Correct Option: 3

Since DE is parallel to BC, by the Basic Proportionality Theorem (or Thales' theorem), we have:

$\frac{AD}{DB} = \frac{AE}{EC}$

Substituting the known values:

$\frac{6}{4} = \frac{9}{EC}$

Cross-multiplying gives:

$6 \cdot EC = 4 \cdot 9$

$6 \cdot EC = 36$

Dividing both sides by 6:

$EC = 6$ cm.

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In triangle ABCABCABC, points DDD and EEE are on ABABAB and ACACAC respectively such that DEDEDE is parallel to BCBCBC. If AD=6AD = 6AD=6 cm, DB=4DB = 4DB=4 cm, AE=9AE = 9AE=9 cm, then the length of ECECEC (in cm) is: