1. **Problem Statement:** We need to find the length of a rectangular plot where the length and width are in the ratio 4:3, and the total cost of fencing the plot is 1680. The cost per meter of fencing is 30. 2. **Formula and Important Rules:** The cost of fencing is calculated by multiplying the perimeter of the plot by the cost per meter. The perimeter $P$ of a rectangle with length $L$ and width $W$ is given by: $$P = 2(L + W)$$ Given the ratio of length to width is 4:3, we can write: $$L = 4x, \quad W = 3x$$ 3. **Calculate the perimeter using the ratio:** $$P = 2(4x + 3x) = 2(7x) = 14x$$ 4. **Relate cost to perimeter:** The total cost is given by: $$\text{Cost} = P \times \text{cost per meter}$$ Substitute the values: $$1680 = 14x \times 30$$ 5. **Solve for $x$:** $$1680 = 420x$$ $$x = \frac{1680}{420} = 4$$ 6. **Find the length:** $$L = 4x = 4 \times 4 = 16$$ **Final Answer:** The length of the plot is 16 meters.