It is given that , with BC QR =1 4 then, ar ar ( PRQ ) ar ( ABC )… - Vidyadip

MCQ

It is given that $\triangle\text{ABC}\sim\text{PQR}$, with $\frac{\text{BC}}{\text{QR}}=\frac{1}{4}$ then, $\text{ar }\frac{\text{ar}\text({\triangle{\text{PRQ}}})}{\text{ar}\text({\text{ABC}})}$ is equal to :

✓
$16$
B
$4$
C
$\frac{1}{4}$
D
$\frac{1}{16}$

✓

Answer

Correct option: A.

$16$

Given,
$\triangle\text{ABC}\sim\triangle\text{PQR}$
and$\frac{\text{BC}}{\text{QR}}=\frac{1}{4}$
Ratio of area of similar triangles is equal to the square of its corresponding sides.
So, $\frac{\text{ar}\text({\triangle{\text{PRQ}}})}{\text{ar}\text({\text{ABC}})}$
$=\Bigg(\frac{\text{QR}}{\text{BC}}\Bigg)^2=\Bigg(\frac{4}{1}\Bigg)^2=16$

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