1. **State the problem:** We have two similar triangles $ABC$ and $PQR$ with sides $AB=5.5$, $BC=5$, $CA=2.5$, and $PQ=16.5$, $QR=15$, $PR=n$. We need to find $n$. 2. **Recall the property of similar triangles:** Corresponding sides of similar triangles are proportional. This means: $$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{CA}{PR}$$ 3. **Calculate the scale factor:** Using the known sides, $$\frac{AB}{PQ} = \frac{5.5}{16.5} = \frac{1}{3}$$ 4. **Check the ratio for the other pair to confirm similarity:** $$\frac{BC}{QR} = \frac{5}{15} = \frac{1}{3}$$ 5. **Use the ratio to find $n$:** $$\frac{CA}{PR} = \frac{2.5}{n} = \frac{1}{3}$$ 6. **Solve for $n$:** $$2.5 = \frac{1}{3} n$$ Multiply both sides by 3: $$3 \times 2.5 = \cancel{3} \times \frac{1}{\cancel{3}} n$$ $$7.5 = n$$ **Final answer:** $$n = 7.5$$