MCQ
$\triangle\text{PQR}\sim\triangle\text{XYZ}$ and the perimeters $\triangle\text{PQR}\sim\triangle\text{XYZ}$ are $30\ cm$ and $18\ cm$ respectively. If $QR = 9\ cm,$ then $,YZ$ is equal to :
- ✓$5.4\ cm.$
- B$12.5\ cm.$
- C$9.5\ cm.$
- D$4.5\ cm.$
✓
Answer
Correct option: A.
$5.4\ cm.$
Given : $\triangle\text{PQR}\sim\triangle\text{XYZ}$
$\therefore\frac{\text{Permeter of }\triangle\text{PQR}}{\text{Permeter of }\triangle\text{XYZ}}=\frac{\text{QR}}{\text{YZ}}$
$\Rightarrow\frac{30}{18}=\frac{9}{\text{YZ}}$
$\Rightarrow\text{YZ}=5.4\text{ cm}$
$\therefore\frac{\text{Permeter of }\triangle\text{PQR}}{\text{Permeter of }\triangle\text{XYZ}}=\frac{\text{QR}}{\text{YZ}}$
$\Rightarrow\frac{30}{18}=\frac{9}{\text{YZ}}$
$\Rightarrow\text{YZ}=5.4\text{ cm}$
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