1. **State the problem:** We have three ropes with lengths in the ratio 7 : 4 : 9. The longest rope is 63 meters. We need to find the difference in length between the other two ropes. 2. **Identify the ratio and variables:** Let the common multiplier be $x$. Then the lengths are: $$7x, 4x, 9x$$ 3. **Use the given longest rope length:** The longest rope corresponds to $9x$, and it is given as 63 meters. $$9x = 63$$ 4. **Solve for $x$:** $$x = \frac{63}{9} = 7$$ 5. **Find the lengths of the other two ropes:** $$7x = 7 \times 7 = 49 \text{ meters}$$ $$4x = 4 \times 7 = 28 \text{ meters}$$ 6. **Calculate the difference between these two ropes:** $$49 - 28 = 21 \text{ meters}$$ **Final answer:** The difference in length between the other two ropes is **21 meters**. --- Regarding the trapezium PQRS, the problem statement seems incomplete or contains a typo (UT is mentioned but not defined in the trapezium). Please provide more details if you want help with that part.