A rectangular plot has a length that is 3 times its width. If the perimeter is 64 meters, find the dimensions of the plot.
["How to Find the Dimensions of a Rectangular Plot: Solving a Perimeter Problem", "When dealing with real estate, landscaping, or construction projects, understanding the dimensions of a rectangular plot is essential. One common problem is determining the length and width of a rectangle when you know that the length is three times the width and the perimeter is 64 meters. This practical question helps build fundamental algebra skills while solving a real-world scenario.", "### Understanding the Problem", "We are told that:", "- The length (L) of the rectangular plot is 3 times its width (W)\n- The perimeter (P) is 64 meters\n- We are to find the exact dimensions: length and width", "### Mathematical Background", "The perimeter of a rectangle is calculated using the formula:", "[\nP = 2 \ imes (L + W)\n]", "Given that ( L = 3W ), we substitute this into the perimeter formula:", "[\n64 = 2 \ imes (3W + W)\n]", "### Step-by-Step Solution", "1. Substitute length:\n [\n 64 = 2 \ imes (3W + W)\n ]", "2. Simplify inside the parentheses:\n [\n 64 = 2 \ imes 4W\n ]\n [\n 64 = 8W\n ]", "3. Solve for width:\n [\n W = \frac{64}{8} = 8 \ ext{ meters}\n ]", "4. Find the length using ( L = 3W ):\n [\n L = 3 \ imes 8 = 24 \ ext{ meters}\n ]", "### Final Dimensions", "- Width = 8 meters\n- Length = 24 meters", "### Why This Matters", "Knowing the exact dimensions helps in estimating fencing costs, planning landscaping, or designing structures. Whether you're building a garden, installing a sports field, or planning real estate, solving such problems ensures precise measurements and efficient resource use.", "### Summary", "- Given: Perimeter = 64 m, ( L = 3W )\n- Calculation leads to: Width = 8 m, Length = 24 m\n- This classic problem demonstrates how algebraic expressions simplify real-life measurements.", "---", "Keywords for SEO: rectangular plot dimensions, find width and length, perimeter calculation, algebra problem, real estate measurements, solve rectangle perimeter, width and length problem, 64 meter perimeter formula", "Understanding and solving rectangular plot problems strengthens your geometric reasoning and prepares you for more complex design and measurement tasks."]
