Question

$Inthe\Delta ABC,DE||BCand\frac{AD}{DB}=\frac{6}{7}.$ If $AC=13cm$, then $EC=$____

• A. 14 cm
• B. 7 cm
• C. 21
• D. 6 cm

Answer 1

The correct option is B 7 cm


In $△$ABC,
DE || BC (Given)

$\therefore \frac{AD}{DB}=\frac{AE}{EC}$ [By BPT]

Adding 1 on both sides we get,

$\frac{AD}{DB}+1=\frac{AE}{EC}+1$

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

$\Rightarrow \frac{AB}{DB}=\frac{AC}{EC}$

$\because$ AB = AD + DB
= 6 + 7
= 13

$\Rightarrow \frac{13}{7}=\frac{13}{EC}$

$\Rightarrow EC=7cm$