Question

If $△ABC$ and $△PQR$ are similar and $\frac{BC}{QR}=\frac{1}{3}$ find $\frac{area\left(PQR\right)}{area\left(BCA\right)}$

• A. $9$
• B. $3$
• C. $\frac{1}{3}$
• D. $\frac{1}{9}$

Answer 1

The correct option is A $9$

$△ABC$ & $△PQR$ are similar.

$\therefore \frac{AB}{PQ}=\frac{BC}{QR}=\frac{1}{3}$

$\therefore \frac{\text{Area}\left(PQR\right)}{\text{Area}\left(BCA\right)}=(\frac{QR}{BC}{)}^2$

$\frac{Area\left(PQR\right)}{Area\left(BCA\right)}={\left(\frac{3}{1}\right)}^2=9$