MCQ
In $\triangle\text{ABC}\sim\triangle\text{DEF}$ and the perimeters of $\triangle\text{ABC}$ and $\triangle\text{DEF}$ are $30\ cm$ and $18\ cm$ respectively. If $BC = 9\ cm$ then $EF =?$
- A$6.3\ cm$
- ✓$5.4\ cm$
- C$7.2\ cm$
- D$4.5\ cm$
✓
Answer
Correct option: B.
$5.4\ cm$
$\triangle\text{ABC}\sim\triangle\text{DEF}$
$\Rightarrow\frac{\text{Perimeters of }\triangle\text{ABC}}{\text{Perimeters of }\triangle\text{DEF}}=\frac{\text{BC}}{\text{EF}}$
$\Rightarrow\frac{30}{18}=\frac{9}{\text{EF}}$
$\Rightarrow\frac{9\times18}{\text{30}}$
$\Rightarrow\text{EF}=5.4\text{cm}$
$\Rightarrow\frac{\text{Perimeters of }\triangle\text{ABC}}{\text{Perimeters of }\triangle\text{DEF}}=\frac{\text{BC}}{\text{EF}}$
$\Rightarrow\frac{30}{18}=\frac{9}{\text{EF}}$
$\Rightarrow\frac{9\times18}{\text{30}}$
$\Rightarrow\text{EF}=5.4\text{cm}$
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