Question

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

Answer 1

$△XYZ\sim △PQR$ [Given]
$\therefore \frac{XY}{PQ}=\frac{YZ}{QR}=\frac{XZ}{PR}$ [Corresponding sides of similar triangles]
$\therefore \frac{4}{8}=\frac{6}{QR}=\frac{5}{PR}$
Now, $\frac{4}{8}=\frac{6}{QR}$
$\therefore QR=\frac{6\times 8}{4}$
$\therefore QR=12cm$
$$\therefore PR=\frac{5\times 8}{4}$$
$$\therefore PR=10cm$$
$\therefore QR=12cm,PR=10cm$