CUET CUET General Test 2024 - 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: | PYQs + Solutions

CUET General Test 2024

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.