In ,DE | BC so that AD = 2.4 cm, AE = 3.2 cm and EC = 4.8 cm. The… - Vidyadip

MCQ

In $\triangle\text{ABC},\text{DE }\|\text{ BC}$ so that $AD = 2.4\ cm, AE = 3.2\ cm$ and $EC = 4.8\ cm$. Then $,AB =?$

A
$3.6\ cm$
✓
$6\ cm$
C
$6.4\ cm$
D
$7.2\ cm$

✓

Answer

Correct option: B.

$6\ cm$

In $\triangle\text{ABC},\text{DE }\|\text{ BC}$
By Basic Proportionality theorem,
$\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
$\Rightarrow\frac{2.4}{\text{DB}}=\frac{3.2}{4.8}$
$\Rightarrow\text{BD}=\frac{2.4\times4.8}{3.2}$
$\Rightarrow\text{BD}=3.6\text{ cm}$
$\text{AB}=\text{AD}+\text{DB}$
$=2.4+3.6=6\text{ cm}$

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