Originally Posted by

**Archie Meade** Yes, that's fine.

You can think of the sides of LMN are magnified by the exact same amount

to be the sides of PQR.

Let k be the magnification factor

$\displaystyle k[MN]=[QR]\Rightarrow\ k=\frac{[QR]}{[MN]}$

$\displaystyle k[LM]=[PQ]\Rightarrow\ k=\frac{[PQ]}{[LM]}$

$\displaystyle k[LN]=[PQ]\Rightarrow\ k=\frac{[PQ]}{[LN]}$

Therefore

$\displaystyle \frac{y}{12}=\frac{x}{18}=\frac{20}{15}$

or

$\displaystyle \frac{y}{20}=\frac{12}{15}$

$\displaystyle \frac{x}{20}=\frac{18}{15}$