A rectangular plot of land has a length that is 3 times its width. If the perimeter of the plot is 400 meters, what is the area of the plot?
["A rectangular plot of land has a length that is 3 times its width. If the perimeter of the plot is 400 meters, what is the area of the plot?", "Ever wondered how a simple geometric shape like a rectangular plot holds real-world value—especially when tied to growing land prices and urban development trends across the U.S.? If you’re exploring land investment, smart growth patterns, or property calculations, you might ask: given a rectangular plot where the length is three times the width and the total perimeter is 400 meters, what is the area? This question reflects rising interest in how geometry influences real estate decisions—no flashy marketing, just clear facts.", "Why This Problem Is Gaining Attention in the U.S.", "In recent years, precise land measurements have become key for investors, urban planners, and homeowners alike. With rising development costs and limited developable space in expanding metro areas, understanding foundational geometry helps inform smart purchases and resource planning. When a rectangular plot has a length three times its width and a defined perimeter—like 400 meters—calculating the area becomes crucial for budgeting and design. This problem isn’t just academic; it reflects the growing curiosity around land efficiency in fast-developing regions of the United States.", "How to Calculate the Area: Step-by-Step Explanation", "To find the area, start by letting the width be \( w \) meters. Since the length is three times the width, the length equals \( 3w \). A rectangle’s perimeter is calculated using the formula:", "\[\nP = 2(\ ext{length} + \ ext{width}) = 2(3w + w) = 2(4w) = 8w\n\]", "Given that the perimeter is 400 meters:", "\[\n8w = 400\n\]", "Solving for \( w \):", "\[\nw = \frac{400}{8} = 50 \ ext{ meters}\n\]", "Now, the length is:", "\[\n3w = 3 \ imes 50 = 150 \ ext{ meters}\n\]", "Finally, the area \( A \) of the rectangle is:", "\[\nA = \ ext{length} \ imes \ ext{width} = 150 \ imes 50 = 7,500 \ ext{ square meters}\n\]", "This clear breakdown shows how basic math directly applies to land assessment—ideal for learners interested in data-driven decisions.", "Common Questions About the Plot Area Calculation", "H3: What if the numbers were different? \nAdjusting the perimeter changes both dimensions proportionally. For any rectangular plot where length = 3 × width and perimeter = \( P \), solving \( 8w = P \) gives \( w = P/8"]
