1. **State the problem:** We are given a rectangular land where the length is 10 meters longer than the breadth. The cost of fencing the land with 3 rounds at 50 per meter totals 13,800. We need to find the length and breadth. 2. **Define variables:** Let the breadth be $x$ meters. Then the length is $x + 10$ meters. 3. **Formula for perimeter:** The perimeter $P$ of a rectangle is given by: $$P = 2(\text{length} + \text{breadth})$$ 4. **Total fencing length:** Since there are 3 rounds of fencing, total fencing length is: $$3 \times P = 3 \times 2(x + (x + 10)) = 6(2x + 10) = 12x + 60$$ 5. **Cost equation:** Cost = (total fencing length) $\times$ (cost per meter) $$13800 = (12x + 60) \times 50$$ 6. **Solve for $x$:** Divide both sides by 50: $$\frac{13800}{50} = 12x + 60$$ $$\cancel{\frac{13800}{50}} = 12x + 60$$ Calculate left side: $$276 = 12x + 60$$ Subtract 60 from both sides: $$276 - 60 = 12x$$ $$216 = 12x$$ Divide both sides by 12: $$\cancel{\frac{216}{12}} = x$$ $$18 = x$$ 7. **Find length:** $$\text{length} = x + 10 = 18 + 10 = 28$$ **Final answer:** Length = 28 meters, Breadth = 18 meters.