Question

In $△XYZ,$ XY = 4 cm, YZ = 6 cm, XZ = 5 cm, If $△XYZ\sim △PQR$ and PQ = 8 cm then find the lengths of remaining sides of $△PQR.$

Answer 1

$\text{Consider,}△XYZ\sim △PQR$
$\therefore \frac{XY}{PQ}=\frac{YZ}{QR}=\frac{XZ}{PR}$
$\Rightarrow \frac{4}{8}=\frac{6}{QR}=\frac{5}{PR}$
$\Rightarrow \frac{4}{8}=\frac{6}{QR}\text{and}\frac{4}{8}=\frac{5}{PR}$
$\Rightarrow QR=12\text{cm and}PR=10\text{cm}$
Hence, the lengths of remaining sides of $△PQR\text{are 12 and}10\text{cm.}$