ABC PQR such that ar( ABC)=4 ar( P Q R). If B C=12 cm, then Q R= - Vidyadip

MCQ

$\triangle ABC \sim \triangle PQR$ such that $\operatorname{ar}(\triangle ABC)=4 \operatorname{ar}(\triangle P Q R)$. If $B C=12 \ cm$, then $Q R=$

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

✓

Answer

Correct option: C.

$6 \ cm$

Since $\triangle A B C \sim \triangle P Q R$
$\therefore \frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\triangle P Q R)}=\frac{B C^2}{Q R^2}$
$\Rightarrow \frac{4 \operatorname{ar}(\triangle P Q R)}{\operatorname{ar}(\triangle P Q R)}=\frac{12^2}{Q R^2}$
$[\because$ Given, $\operatorname{ar}(\triangle A B C)=4 \operatorname{ar}(\triangle P Q R)]$
$\Rightarrow Q R^2=\frac{144}{4}=36$
$\Rightarrow Q R=6 \ cm $

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