In , D and E are points on side AB and AC respectively such that … - Vidyadip

MCQ

In $\triangle\text{ABC}, D$ and $E$ are points on side $\text{AB}$ and $\text{AC}$ respectively such that $\ce{DE \| BC}$ and $\text{AD : DB} = 3 : 1$. If $\text{EA} = 3.3\ cm,$ then $\text{AC} =$

A
$1.1\ cm.$
B
$4\ cm.$
✓
$4.4\ cm.$
D
$5.5\ cm.$

✓

Answer

Correct option: C.

$4.4\ cm.$

Given: In $\triangle\text{ABC, D}$ and $E$ are points on the side $\text{AB}$ and $\text{AC}$ respectively such that $\ce{DE \| BC}$ and $\text{AD : DB} = 3 : 1$.
Also, $\text{EA} = 3.3\ cm.$
To find: $\text{AC}$

In $\triangle\text{ABC}, \ce{DE \| BC.}$
Using corollory of basic proportionality theorem, we have,
$\frac{\text{AD}}{\text{AB}}=\frac{\text{EA}}{\text{AC}}$
$\frac{\text{AD}}{\text{AD}+\text{BD}}=\frac{3.3}{\text{AC}}$
$\frac{\text{AD}}{\text{AD}+\frac{1}{3}\text{AD}}=\frac{3.3}{\text{AC}}$
$\text{EC}=4.4\text{cm}$
Hence the correct answer is $C$.

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