Choose the correct answer from the given four options: Its is giv… - Vidyadip

MCQ

Choose the correct answer from the given four options: Its is given that $\triangle\text{ABC}\sim\triangle\text{PQR},$ with $\frac{\text{BC}}{\text{QR}}=\frac{1}{3}.$ Then $,\frac{\text{ar}(\text{PQR})}{\text{ar}(\text{BCA})}$ is equal to :

✓
$9$
B
$3$
C
$\frac{1}{3}$
D
$\frac{1}{9}$

✓

Answer

Correct option: A.

$9$

Given, $\triangle\text{ABC}\sim\triangle\text{PQR},$ and $\frac{\text{BC}}{\text{QR}}=\frac{1}{3}.$
We know that the ratio of the areas of two similar triangles is equal to squal of the ratio of their corresponding sides.
$\therefore\frac{\text{ar}(\text{PQR})}{\text{ar}(\text{BCA})}=\frac{(\text{QR})^2}{(\text{BC})^2}$
$\Big(\frac{\text{QR}}{\text{BC}}\Big)^2=\Big(\frac{3}{1}\Big)^2=\frac{9}{1}=9$

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