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
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6
By the Basic Proportionality Theorem (Thales’ theorem), a line drawn parallel to one side of a triangle divides the other two sides in the same ratio. Since DE is parallel to BC, \(\displaystyle\frac{AD}{DB}=\frac{AE}{EC}\). The small triangle ADE is the big triangle ABC on a smaller scale, which is why the sides are cut in the same ratio.
Putting in the given lengths: \(\displaystyle\frac{6}{4}=\frac{9}{EC}\)
\(\displaystyle EC=\frac{9\times4}{6}=6\,\mathrm{cm}\)