If ∆ABC and ∆PQR are similar and $$\frac{BC}{QR}=\frac{1}{3}$$​, find $$\frac{ar(∆PQR)}{ar(∆BCA)}$$​​

Correct option is A

Given:

△ABC and △PQR are similar.

The ratio of corresponding sides is $$\frac{BC}{QR} = \frac{1}{3}.$$​​

Concept Used:

​$$\frac{\text{ar}(\triangle PQR)}{\text{ar}(\triangle ABC)} = \left( \frac{QR}{BC} \right)^2$$​​

Solution:

Given,$$\frac{BC}{QR} = \frac{1}{3}$$​, we can substitute this into the formula for the ratio of the areas:

​$$\frac{\text{ar}(\triangle PQR)}{\text{ar}(\triangle ABC)} = \left( \frac31\right)^2 = 9$$