Given: triangleMLN, overline(ML)=13, overline(MN)=6, overline(NL)=10, triangleRQS, overline(RQ)=39, overline(RS)=18

Given:
$$\displaystyle\triangle{M}LN,\overline{{{M}{L}}}={13},\overline{{{M}{N}}}={6},\overline{{{N}{L}}}={10},\triangle{R}{Q}{S},\overline{{{R}{Q}}}={39},\overline{{{R}{S}}}={18},\overline{{{S}{Q}}}={30}$$
Find the scale factor from $$\displaystyle\triangle{M}LN$$ to $$\displaystyle\triangle{R}{Q}{S}$$.

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Aamina Herring
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
$$\displaystyle\frac{\overline{{{R}{S}}}}{\overline{{{M}{N}}}}=\frac{{18}}{{6}}={3}$$
$$\displaystyle\frac{\overline{{{S}{Q}}}}{\overline{{{N}{L}}}}=\frac{{30}}{{10}}={3}$$