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 perimeter $P$ of a rectangle is given by $$P = 2(\text{length} + \text{width})$$ - The cost of fencing is calculated by multiplying the perimeter by the cost per meter. 3. **Assign Variables:** Let the length be $4x$ and the width be $3x$ since the ratio is 4:3. 4. **Calculate Perimeter:** $$P = 2(4x + 3x) = 2(7x) = 14x$$ 5. **Calculate Total Cost:** Cost = Perimeter $\times$ Cost per meter $$1680 = 14x \times 30$$ 6. **Solve for $x$:** $$1680 = 420x$$ $$x = \frac{1680}{420} = 4$$ 7. **Find Length:** Length = $4x = 4 \times 4 = 16$ meters. **Final Answer:** The length of the plot is 16 meters.