A rectangular plot of land has a length that is 3 times its width. If the area of the plot is 192 square meters, what is the width of the plot?
["Title: How to Calculate the Width of a Rectangular Land Plot Using Area and Length-Width Relationship", "When dealing with real estate, construction projects, or land development, one fundamental question often arises: what is the width of a rectangular plot when its length is three times its width and the area is known? Understanding this relationship helps in precise planning, budgeting, and land use.", "In this article, we’ll walk through a clear, step-by-step solution to a common problem: a rectangular plot where the length is 3 times the width, and the total area is 192 square meters. We’ll also explain how to derive the width mathematically — a crucial skill for architects, engineers, and property owners alike.", "---", "### Understanding the Problem", "Let’s define the variables clearly:", "- Let the width of the rectangular plot be ( w ) meters.\n- Then, the length is ( 3w ) meters (since it’s 3 times the width).\n- The area of a rectangle is calculated by:\n [\n \ ext{Area} = \ ext{Length} \ imes \ ext{Width}\n ]\n- Substituting the expressions:\n [\n 192 = 3w \ imes w = 3w^2\n ]", "---", "### Step-by-Step Equation Solving", "Start with the equation:\n[\n3w^2 = 192\n]", "Step 1: Divide both sides by 3 to isolate ( w^2 ):\n[\nw^2 = \frac{192}{3} = 64\n]", "Step 2: Take the square root of both sides:\n[\nw = \sqrt{64} = 8\n]", "Since width must be a positive dimension, we disregard the negative root.", "---", "### Final Answer", "The width of the rectangular plot is 8 meters.", "To verify:\n- Width = 8 m → Length = ( 3 \ imes 8 = 24 ) m\n- Area = ( 8 \ imes 24 = 192 ) m² — confirmed correct.", "---", "### Why This Matters in Real-World Applications", "Knowing how to work with variables and area equations empowers decision-makers to:", "- Optimize land use in farming and development\n- Calculate construction costs based on usable space\n- Design structures that fit precisely within a plot\n- Ensure compliance with zoning regulations and building codes", "Whether you’re a homeowner purchasing property, a planner laying out a community space, or a contractor estimating costs, understanding the connection between dimensions and area is both practical and essential.", "---", "### Key Takeaways", "- Define width as ( w ), then express length as ( 3w ).\n- Use the area formula: ( \ ext{Area} = 3w \ imes w = 3w^2 ).\n- Solve for ( w ) by reorganizing into ( w = \sqrt{\frac{\ ext{Area}}{3}} ).\n- Apply square roots and verify your answer for accuracy.", "Mastering this simple algebraic method saves time, reduces errors, and supports smarter land-based decisions.", "---", "If you’re working with irregular plots or different length-to-width ratios, similar steps apply — just adjust the equation accordingly. Understanding these principles is key to confidence in land measurement and planning."]
