A rectangular plot of land has a length that is 3 times its width. If the perimeter of the plot is 64 meters, what are the dimensions of the plot?
["Rectangular Plot Dimensions: How to Calculate Length and Width When Perimeter is Known", "If you’ve ever been tasked with determining the size of a rectangular plot based on a given perimeter, you’re not alone — this is a common real-world problem in construction, landscaping, and urban planning. In this article, we’ll walk through how to find the dimensions of a rectangular plot where the length is 3 times the width, and the perimeter is 64 meters.", "---", "### Understanding the Problem", "We’re told:", "- The length (L) is 3 times the width (W)\n- The perimeter (P) of the rectangle is 64 meters", "Our goal is to calculate the exact dimensions — width and length — of the plot.", "---", "### Step 1: Use the Perimeter Formula for a Rectangle", "The formula for the perimeter of a rectangle is:", "[\nP = 2(L + W)\n]", "We’re given that ( P = 64 ), so:", "[\n2(L + W) = 64\n]", "Divide both sides by 2:", "[\nL + W = 32 \quad \ ext{(Equation 1)}\n]", "---", "### Step 2: Use the Given Relationship Between Length and Width", "We’re told that:", "[\nL = 3W\n]", "---", "### Step 3: Substitute and Solve", "Substitute ( L = 3W ) into Equation 1:", "[\n3W + W = 32\n]", "[\n4W = 32\n]", "[\nW = 8\n]", "Now substitute ( W = 8 ) back into ( L = 3W ):", "[\nL = 3 \ imes 8 = 24\n]", "---", "### ✅ Final Answer", "- Width of the plot: 8 meters\n- Length of the plot: 24 meters", "---", "### Why This Matters", "Solving problems like this strengthens your ability to apply geometry to practical scenarios. Whether you're planning a garden, a backyard redesign, or commercial property development, understanding how dimensions relate through formulas helps you make accurate measurements and informed decisions.", "---", "### Key Takeaways", "- Given perimeter and a proportional relationship between length and width, substitute to form equations.\n- Use algebra to express one variable in terms of the other.\n- Calculate using basic arithmetic — a foundational skill for surveying, carpentry, architecture, and landscaping.", "---", "Remember: A rectangular plot with a perimeter of 64 meters and length 3 times width measures 8 meters wide by 24 meters long — perfect for planning your next outdoor project!", "---", "If you want to learn more about calculating land area or optimizing rectangular spaces, explore our guides on rectangle geometry, perimeter calculations, and real estate land measurements. Happy building!"]
