A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 meters, find the dimensions of the rectangle.
["# Finding the Dimensions of a Rectangle: A Practical Geometry Problem", "When dealing with rectangles, one of the most fundamental yet powerful relationships involves the relationship between the length, width, and perimeter. A classic geometry problem often used in teaching and practical applications is: A rectangle has a length that is 3 times its width, and its perimeter is 48 meters. What are the rectangle’s dimensions?", "In this article, we’ll break down how to solve this classic rectangle problem step-by-step, reinforcing key concepts in algebra and geometry while helping you understand how to find dimension values from real-world constraints.", "## Understanding the Problem", "We’re told:", "- The length (( L )) is 3 times the width (( W )):\n [\n L = 3W\n ]", "- The perimeter (( P )) is 48 meters:\n [\n P = 48 \ ext{ meters}\n ]", "The formula for the perimeter of a rectangle is:\n[\nP = 2L + 2W\n]", "Substituting the perimeter and the length relationship into the formula gives us a solvable equation.", "## Writing the Equation", "Substitute ( L = 3W ) into the perimeter formula:", "[\n2L + 2W = 48\n]\n[\n2(3W) + 2W = 48\n]", "Simplify the equation:", "[\n6W + 2W = 48\n]\n[\n8W = 48\n]", "## Solving for the Width", "Divide both sides by 8:", "[\nW = \frac{48}{8} = 6 \ ext{ meters}\n]", "## Finding the Length", "Now, use ( L = 3W ):", "[\nL = 3 \ imes 6 = 18 \ ext{ meters}\n]", "## Final Dimensions", "The width of the rectangle is 6 meters, and the length is 18 meters.", "Verify the perimeter:", "[\n2L + 2W = 2(18) + 2(6) = 36 + 12 = 48 \ ext{ meters} \quad \ ext{✔}\n]", "This confirms our solution is correct.", "## Why This Matters — Real-World Applications", "Understanding how to relate dimensions through ratios and formulas like perimeter is essential in architecture, interior design, agriculture, and countless other fields. Knowing how to convert a ratio into concrete measurements empowers practical problem-solving.", "## Summary", "- Length is 3 times the width\n- Perimeter formula: ( P = 2L + 2W )\n- Using substitution and algebra, solved ( W = 6 ) meters and ( L = 18 ) meters\n- Check confirmed: Perimeter = 48 meters", "If you’re facing a similar problem, always express one dimension via the given ratio and substitute into the perimeter formula—this method applies broadly to rectangular geometry tasks.", "---", "Key Takeaways:\n- Use the ratio to set up a variable equation.\n- Substitute known relationships into standard formulas.\n- Simplify and solve algebraically.\n- Always verify by recomputing the perimeter.", "Whether you're solving math problems for homework or designing a structure, mastering these steps builds confidence in geometry and real-life measurement challenges."]
