A rectangular plot of land has a length that is twice its width. If the perimeter is 180 meters, find the area of the plot.
["Optimize Your Land Use: Finding the Area of a Rectangular Plot with Given Dimensions", "When managing land or planning construction projects, understanding the relationship between a rectangle’s perimeter, dimensions, and area is essential. A common real-world problem involves rectangular plots where one dimension relates directly to the other—such as when a plot’s length is twice its width and the perimeter measures 180 meters. This scenario allows for precise calculations that help estimate land area efficiently.", "---", "### The Problem: A Rectangular Plot with Known Ratio and Perimeter", "We are given:\n- The length ($ L $) is twice the width ($ W $):\n [\n L = 2W\n ]\n- The perimeter ($ P $) is 180 meters:\n [\n P = 180 \ ext{ meters}\n ]", "Our goal is to find the area of the rectangular plot using these constraints.", "---", "### Step 1: Use the Perimeter Formula for a Rectangle", "The perimeter $ P $ of a rectangle is given by:\n[\nP = 2(L + W)\n]", "Substitute $ L = 2W $ into the formula:\n[\n180 = 2(2W + W) = 2(3W) = 6W\n]", "---", "### Step 2: Solve for the Width ($ W $)", "[\n6W = 180\n\Rightarrow W = \frac{180}{6} = 30 \ ext{ meters}\n]", "---", "### Step 3: Find the Length ($ L $)", "Using $ L = 2W $:\n[\nL = 2 \ imes 30 = 60 \ ext{ meters}\n]", "---", "### Step 4: Calculate the Area", "The area $ A $ of a rectangle is:\n[\nA = L \ imes W = 60 \ imes 30 = 1800 \ ext{ square meters}\n]", "---", "### Why This Calculation Matters", "Understanding how to derive area from perimeter and proportional relationships is vital in construction, agriculture, real estate, and urban planning. When a landowner or developer knows the shape’s proportions, efficient resource use—like fencing, grading, or building—becomes much easier.", "Key takeaways:\n- If length is twice the width and the perimeter is 180 m, the width is 30 m and length is 60 m.\n- The area of the plot is 1800 square meters—a clear, exact measure for planning.", "---", "### Summary", "| Parameter | Value |\n|---------------|-------------|\n| Width ($ W $)| 30 meters |\n| Length ($ L $)| 60 meters |\n| Perimeter ($ P $)| 180 meters |\n| Area ($ A $) | 1800 m² |", "Now you can confidently use rectangular land calculations in your projects—turning simple geometry into practical insights every time.", "---", "Keywords for SEO: rectangular plot area calculation, rectangular landエリア with perimeter, how to find area from perimeter and ratio, land area formula, 180 meter perimeter rectangle, width and length relationship, real estate land planning."]
