Question

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

Answer 1

Consider, $∆$ XYZ ~ $∆$ PQR
$$\begin{gathered} \therefore \frac{\mathrm{XY}}{\mathrm{PQ}}=\frac{\mathrm{YZ}}{\mathrm{QR}}=\frac{\mathrm{XZ}}{\mathrm{PR}} \\ \Rightarrow \frac{4}{8}=\frac{6}{\mathrm{QR}}=\frac{5}{\mathrm{PR}} \\ \Rightarrow \frac{4}{8}=\frac{6}{\mathrm{QR}}\mathrm{and}\frac{4}{8}=\frac{5}{\mathrm{PR}} \end{gathered}$$
$\Rightarrow \mathrm{QR}=12\mathrm{cm}\mathrm{and}\mathrm{PR}=10\mathrm{cm}$
Hence, the lengths of remaining sides of $∆$PQR are 12 and 10 cm.