such that ar( )=4 ar( ). If BC = 12 cm, then QR = - Vidyadip

MCQ

$\triangle\text{ABC}\sim\triangle\text{PQR}$ such that $\text{ar}(\triangle\text{ABC})=4\ \text{ar}(\triangle\text{PQR}).$ If $BC = 12\ cm,$ then $QR =$

A
$9\ cm.$
B
$10\ cm.$
✓
$6\ cm.$
D
$8\ cm.$

✓

Answer

Correct option: C.

$6\ cm.$

Given : $\triangle\text{ABC}\sim\triangle\text{PQR}$ and $BC = 12\ cm$
$\text{ar}(\triangle\text{ABC})=4\ \text{ar}(\triangle\text{PQR})$
Now, $\frac{\text{ar}(\triangle\text{ABC})}{\text{ar}(\triangle\text{PQR})}=\Big(\frac{\text{BC}}{\text{QR}}\Big)^2$
$\Rightarrow\frac{4\text{ar}(\triangle\text{PQR})}{\text{ar}(\triangle\text{PQR})}=\frac{(12)^2}{\text{QR}^2}$
$\Rightarrow\text{QR}^2=\frac{144}{4}$
$\Rightarrow\text{QR}=\frac{12}{2}$
$\Rightarrow\text{QR}=6\text{ cm}.$

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