Three parallel lines l, m and n are cut by one transversal at the points A, B and C respectively, and by a second transversal at the points P, Q and R respectively. If AB = 5 cm, BC = 10 cm and PQ = 6 cm, find QR (in cm).

Parallel lines cut all transversals in the same ratio (the intercept form of BPT), so $\frac{AB}{BC}=\frac{PQ}{QR}$. Then $\frac{5}{10}=\frac{6}{QR}$ and $QR=\frac{6\times 10}{5}=12$ cm. Choosing 6 assumes the second transversal is cut into equal pieces; 3 comes from inverting the proportion; 15 comes from adding the first transversal's two intercepts instead of using the ratio.