A rectangular field has a length that is 3 times its width. If the perimeter of the field is 400 meters, what is the area of the field?
["Rectangular Field Area Calculated Using Perimeter: Solve for Length, Width, and Area", "If you’ve encountered a rectangular field where the length is 3 times the width and the perimeter measures 400 meters, calculating the area is an elegant application of basic geometry and algebra. In this SEO-optimized article, we’ll walk through the step-by-step solution to find the field’s area efficiently—perfect for homeowners, landowners, and agricultural planners seeking precise field measurements.", "---", "### Understanding the Problem", "We’re given:\n- The field is rectangular.\n- Length (L) = 3 × Width (W)\n- Perimeter = 400 meters\n- Goal: Find the area (L × W)", "---", "### Step 1: Use the Perimeter Formula", "The perimeter P of a rectangle is given by:\n[\nP = 2(L + W)\n]\nGiven ( P = 400 ), substitute into the formula:\n[\n400 = 2(L + W)\n]", "Divide both sides by 2:\n[\n200 = L + W\n]", "---", "### Step 2: Substitute Length in Terms of Width", "Since ( L = 3W ), substitute into the equation:\n[\n200 = 3W + W\n]\n[\n200 = 4W\n]", "Solve for W:\n[\nW = \frac{200}{4} = 50 \ ext{ meters}\n]", "---", "### Step 3: Find the Length", "Using ( L = 3W ):\n[\nL = 3 \ imes 50 = 150 \ ext{ meters}\n]", "---", "### Step 4: Calculate the Area", "Area A of a rectangle is:\n[\nA = L \ imes W\n]\n[\nA = 150 \ imes 50 = 7,500 \ ext{ square meters}\n]", "---", "### Final Answer", "The area of the rectangular field is 7,500 square meters.", "---", "### Why This Calculation Matters (SEO & Practical Value)", "Understanding how to derive area from perimeter and ratio relationships is crucial in agriculture, landscaping, construction, and property management. This method applies to countless real-world scenarios—such as designing crop fields, planning garden beds, or budgeting land development. Mastering these algebraic steps boosts both mathematical literacy and practical problem-solving skills.", "---", "Key Terms for SEO Optimization:\n- Rectangular field area calculation\n- Perimeter to area conversion\n- Length and width relationship\n- Field dimensions using algebra\n- How to find area given perimeter and ratio", "By following these clear steps, anyone can quickly determine field sizes from proportional constraints—ideal for farmers, architects, and curious learners.", "---", "Summary:\nFor a rectangle where length is 3 times width and perimeter is 400 meters, solving gives width = 50 m, length = 150 m, and area = 7,500 m². Use this formula for any proportional rectangular field to calculate precise area quickly!"]
