MCQ
In a $\triangle\text{ABC},$ if DE is drawn parallel to BC, cutting AB and AC at D and E respectively such that AB = 7.2cm, AC = 6.4cm and AD = 4.5cm. Then, AE =?
- A5.4cm
- ✓4cm
- C3.6cm
- D3.2cm
✓
Answer
Correct option: B.
4cm
In $\triangle\text{ABC},\text{DE }||\text{ BC}$
By Basic proportionality theorem,
$\frac{\text{AE}}{\text{AC}}=\frac{\text{AD}}{\text{AB}}$
$\Rightarrow\frac{\text{AE}}{6.4}=\frac{4.5}{7.2}$
$\Rightarrow\text{AE}=\frac{4.5\times6.4}{7.2}$
$\Rightarrow\text{AE}=4\text{cm}$
By Basic proportionality theorem,
$\frac{\text{AE}}{\text{AC}}=\frac{\text{AD}}{\text{AB}}$
$\Rightarrow\frac{\text{AE}}{6.4}=\frac{4.5}{7.2}$
$\Rightarrow\text{AE}=\frac{4.5\times6.4}{7.2}$
$\Rightarrow\text{AE}=4\text{cm}$
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