If ABC PQR such that B= Q and C= R, then find ar( ABC) ar( PQR) i… - Vidyadip

MCQ

If $\triangle \text{ABC} \sim \triangle \text{PQR}$ such that $\angle B=\angle Q$ and $\angle C=\angle R$, then find $\frac{\operatorname{ar}(\triangle \text{ABC})}{\operatorname{ar}(\triangle \text{PQR})}$ if $BC=3.5 m$ and $QR=7 cm$.

A
$5$
B
$25$
✓
$2500$
D
$50$

✓

Answer

Correct option: C.

$2500$

Given, $\triangle \text{ABC} \sim \triangle \text{PQR}$
We know, areas of similar triangles are proportional to the squares of corresponding sides.
$\therefore \frac{\operatorname{ar}(\triangle \text{ABC})}{\operatorname{ar}(\triangle \text{PQR})}=\left(\frac{BC}{Q R}\right)^2=\left(\frac{3.5 m }{7 \ cm }\right)^2$
$=\left(\frac{350 \ cm }{7 \ cm }\right)^2$
$=(50)^2$
$=2500$

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