Question

$Inthe\Delta ABC,DE||BCand\frac{AD}{DB}=\frac{2}{5}.$ If $AC=5.6cm$, then $AE=$____

• A. 3 cm
• B. 1.6 cm
• C. 4 cm
• D. 3.5 cm

Answer 1

The correct option is B 1.6 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
= 2 + 5
= 7

$\Rightarrow \frac{7}{5}=\frac{5.6}{EC}$

$\Rightarrow EC=5\times 0.8$
$=4cm$
AC = AE + EC
$\Rightarrow$ 5.6 = AE + 4
$\Rightarrow$ AE = 5.6 - 4 cm
= 1.6 cm