1. **Stating the problem:** Quadrilateral ABCD is similar to quadrilateral PQRS. We need to find: (a) The ratio of the length of AB to the length of PQ in the form $1:n$. (b) The length of RQ. (c) The length of CD. 2. **Similarity rule:** For similar quadrilaterals, corresponding sides are proportional. This means: $$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{CD}{RS} = \frac{AD}{PS}$$ 3. **Given lengths:** - $AB = 5$ cm - $AD = 11$ cm - $PQ = 27.5$ cm - $RS = 42.5$ cm 4. **(a) Find the ratio $1:n$ for $\frac{AB}{PQ}$:** $$\frac{AB}{PQ} = \frac{5}{27.5} = \frac{5}{27.5} = \frac{1}{5.5}$$ So, the ratio is $1 : 5.5$. 5. **(b) Find length of $RQ$:** Since $RQ$ corresponds to $BC$, and $BC = 5$ cm (given as length from B to C), use the ratio: $$\frac{BC}{RQ} = \frac{AB}{PQ} = \frac{1}{5.5}$$ Rearranged: $$RQ = BC \times 5.5 = 5 \times 5.5 = 27.5 \text{ cm}$$ 6. **(c) Find length of $CD$:** $CD$ corresponds to $RS$, and $RS = 42.5$ cm. Using the ratio: $$\frac{CD}{RS} = \frac{1}{5.5} \implies CD = \frac{RS}{5.5} = \frac{42.5}{5.5} = 7.727... \approx 7.73 \text{ cm}$$ **Final answers:** (a) $1 : 5.5$ (b) $27.5$ cm (c) $7.73$ cm