MCQ
In $\triangle\text{ABC}, D$ and $E$ are points on side $AB$ and $AC$ respectively such that $DE \| BC$ and $AD : DB = 3 : 1.$ If $EA = 3.3\ cm,$ then $AC =$
- A$1.1\ cm.$
- B$4\ cm.$
- ✓$4.4\ cm.$
- D$5.5\ cm.$
✓
Answer
Correct option: C.
$4.4\ cm.$
Give $n$ : In $\triangle\text{ABC}, D$ and $E$ are points on the side $AB$ and $AC$ respectively such that $DE \| BC$ and $AD : DB = 3 : 1$.
Also $, EA = 3.3\ cm.$
To find : $AC$
In $\triangle\text{ABC}, DE \| BC.$
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 $C$.
Also $, EA = 3.3\ cm.$
To find : $AC$
In $\triangle\text{ABC}, DE \| BC.$
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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