A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 64 meters, what is the area of the rectangle?
["Title: How to Calculate the Area of a Rectangle Given Its Perimeter and Aspect Ratio", "Understanding basic geometry can significantly simplify solving real-life problems—like calculating the area of a rectangular space when given its perimeter and a fixed length-to-width ratio. In this article, we’ll explore a practical problem: finding the area of a rectangle where the length is three times its width, and the total perimeter is 64 meters.", "### Understanding the Problem", "We are told:\n- The length ( L ) of the rectangle is 3 times its width ( W ):\n [ L = 3W ]\n- The perimeter ( P ) is 64 meters:\n [ P = 64 \ ext{ m} ]\nOur goal is to find the area ( A ) of the rectangle, which is calculated by:\n[ A = L \ imes W ]", "### Step-by-Step Solution", "#### Step 1: Use the Perimeter Formula", "The perimeter of a rectangle is given by:\n[ P = 2L + 2W ]\nSubstitute ( L = 3W ) into the formula:\n[\n64 = 2(3W) + 2W\n]\nSimplify:\n[\n64 = 6W + 2W = 8W\n]", "#### Step 2: Solve for Width", "Divide both sides by 8:\n[\nW = \frac{64}{8} = 8 \ ext{ meters}\n]", "#### Step 3: Find the Length", "Since ( L = 3W ):\n[\nL = 3 \ imes 8 = 24 \ ext{ meters}\n]", "#### Step 4: Calculate the Area", "Now apply the area formula:\n[\nA = L \ imes W = 24 \ imes 8 = 192 \ ext{ m}^2\n]", "### Summary of Results", "| Measurement | Value |\n|-------------|-------|\n| Width (( W )) | 8 m |\n| Length (( L )) | 24 m |\n| Perimeter (( P )) | 64 m |\n| Area (( A )) | 192 m² |", "### Why This Matters", "This type of problem demonstrates how relationships between dimensions affect size properties. Knowing that the length is three times the width allows us to reduce variables and solve efficiently using algebra. Whether designing a room, planning a garden, or planning a construction project, such calculations ensure accurate space utilization.", "### Final Notes", "- Always write down known values and relationships clearly.\n- Use substitution to express everything in terms of one variable.\n- Verify units remain consistent throughout calculations.", "By following these steps, you not only solve for the area but also gain confidence in handling geometric word problems.", "Keywords: rectangle perimeter formula, calculate rectangle area, 3 times width rectangle, rectangle dimensions formula, geometry problem solution, real-life geometry applications, how to find area of rectangle with given perimeter and ratio.\nMeta Description: Learn how to find the area of a rectangle when its length is three times its width and perimeter is 64 meters. Step-by-step calculation includes solving for width, length, and area. Perfect for geometry practice."]
