Question

$\Delta ABC\sim \Delta PQR$ and $\frac{area\Delta ABC}{area\Delta PQR}=\frac{16}{9}$. If PQ=18 cm and BC=12cm, then AB and QR are respectively

• A. 9 cm, 24 cm
• B. 24 cm, 9 cm
• C. 32 cm, 6.75 cm
• D. 13.5 cm, 16 cm

Answer 1

The correct option is B 24 cm, 9 cm

Given that $\frac{areaof\Delta ABC}{areaof\Delta PQR}$
$=\frac{16}{9}={\left(\frac{AB}{PQ}\right)}^2={\left(\frac{BC}{QR}\right)}^2$
$\Rightarrow \frac{16}{9}={\left(\frac{AB}{PQ}\right)}^2\Rightarrow AB=24cm$
Also, $\frac{16}{9}={\left(\frac{12}{QR}\right)}^2\Rightarrow QR=9cm$