MCQ
$\triangle\text{ABC}\sim\triangle\text{DEF}$ and their perimeters are $32\ cm$ and $24\ cm$ respectively. If $AB = 10\ cm$ then $DE =?$
- A$8\ cm$
- ✓$7.5\ cm$
- C$15\ cm$
- D$5\sqrt{3}\text{cm}$
✓
Answer
Correct option: B.
$7.5\ cm$
$\therefore\triangle\text{ABC}\sim\triangle\text{DEF}$
$\therefore\frac{\text{Perimeter}(\triangle\text{ABC})}{\text{Perimeter}(\triangle\text{DEF})}=\frac{\text{AB}}{\text{DE}}$
$\Rightarrow\frac{32}{24}=\frac{10}{\text{DE}}$
$\Rightarrow\text{DE}=\frac{10\times24}{\text{32}}=7.5\text{cm}$
$\therefore\frac{\text{Perimeter}(\triangle\text{ABC})}{\text{Perimeter}(\triangle\text{DEF})}=\frac{\text{AB}}{\text{DE}}$
$\Rightarrow\frac{32}{24}=\frac{10}{\text{DE}}$
$\Rightarrow\text{DE}=\frac{10\times24}{\text{32}}=7.5\text{cm}$
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