Question

$Inthe\Delta ABC,DE||BCand\frac{AD}{DB}=\frac{3}{5}.$ If $AC=5.6cm$, then $AE=$____

• A. 3.5 cm
• B. 2.5 cm
• C. 2.1 cm
• D. 2 cm

Answer 1

The correct option is C 2.1 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
= 3 + 5
= 8

$\Rightarrow \frac{8}{5}=\frac{5.6}{EC}$

$\Rightarrow EC=5\times 0.7$
$=3.5cm$
AC = AE + EC
$\Rightarrow$ 5.6 = AE + 3.5
$\Rightarrow$ AE = 5.6 - 3.5 cm
= 2.1 cm