The scale factor from \(\displaystyle\triangle{M}{\ln{}}\) to \(\displaystyle\triangle{R}{Q}{S}\) is found by dividiing each of \(\displaystyle\triangle{R}{Q}{S}\) by the similar side in \(\displaystyle\triangle{R}{Q}{S}\).

\(\displaystyle\frac{\overline{{{R}{Q}}}}{\overline{{{M}{L}}}}=\frac{{39}}{{13}}={3}\)

The scale factor is 3. To verify, apply to other sides

\(\displaystyle\frac{\overline{{{R}{S}}}}{\overline{{{M}{N}}}}=\frac{{18}}{{6}}={3}\)

\(\displaystyle\frac{\overline{{{S}{Q}}}}{\overline{{{N}{L}}}}=\frac{{30}}{{10}}={3}\)

\(\displaystyle\frac{\overline{{{R}{Q}}}}{\overline{{{M}{L}}}}=\frac{{39}}{{13}}={3}\)

The scale factor is 3. To verify, apply to other sides

\(\displaystyle\frac{\overline{{{R}{S}}}}{\overline{{{M}{N}}}}=\frac{{18}}{{6}}={3}\)

\(\displaystyle\frac{\overline{{{S}{Q}}}}{\overline{{{N}{L}}}}=\frac{{30}}{{10}}={3}\)