The perimeter is given by \( 2(w + 3w) = 96 \).
["Solving the Perimeter Equation: How to Solve “The Perimeter is Given by ( 2(w + 3w) = 96 )”", "Understanding how to solve perimeter problems is essential in geometry, especially when working with unknown dimensions and formulae. One common equation students encounter is:", "[\n2(w + 3w) = 96\n]", "This equation represents the perimeter of a rectangle where ( w ) is the width and ( 3w ) is the length. In this article, we’ll explore how to solve this equation step by step, explain its meaning, and highlight why mastering perimeter calculations is valuable in real-world applications.", "---", "### Understanding the Perimeter Formula", "The perimeter of a rectangle is calculated using the formula:", "[\n\ ext{Perimeter} = 2 \ imes (\ ext{length} + \ ext{width})\n]", "Given that the length is ( 3w ) and the width is ( w ), substitute these into the formula:", "[\n2(w + 3w) = 96\n]", "Simplify inside the parentheses:", "[\nw + 3w = 4w\n]", "So the equation becomes:", "[\n2(4w) = 96\n]", "---", "### Solving for ( w )", "Multiply ( 2 \ imes 4w ):", "[\n8w = 96\n]", "Now divide both sides by 8 to isolate ( w ):", "[\nw = \frac{96}{8} = 12\n]", "Thus, the width ( w ) is 12 units. Since the length is ( 3w ), calculate:", "[\n\ ext{Length} = 3w = 3 \ imes 12 = 36\n]", "---", "### Verifying the Solution", "Plug ( w = 12 ) back into the original perimeter equation:", "[\n2(12 + 36) = 2(48) = 96\n]", "The equation holds true, confirming that the solution is correct.", "---", "### Real-World Applications of Perimeter Problems", "Calculating the perimeter of shapes is crucial in everyday life and many professional fields:", "- Interior design and construction: Accurately measuring room boundaries to estimate material needs like flooring or baseboards.\n- Farming and landscaping: Determining the length of fencing required around fields or garden beds.\n- Math education: Building foundational algebra skills through real-life word problems.", "---", "### Key Takeaways", "- The expression ( 2(w + 3w) = 96 ) models the perimeter of a rectangle where the length is three times the width.\n- Simplify the expression first: ( w + 3w = 4w ), then solve ( 8w = 96 ) to find ( w = 12 ).\n- Always verify your solution by substituting back into the original equation.\n- Perimeter problems are practical tools in STEM, architecture, and day-to-day calculations.", "---", "### Summary", "Solving the equation ( 2(w + 3w) = 96 ) demonstrates how algebraic reasoning and geometric formulas work together to find unknown dimensions. By simplifying expressions, performing arithmetic operations, and verifying results, students strengthen both mathematical fluency and problem-solving skills. Whether measuring a room, building a garden, or tackling algebra homework, mastering perimeter calculations is a valuable skill for academic and real-world success.", "---", "Meta Title: Solve the Perimeter Equation: ( 2(w + 3w) = 96 ) ✔️ Step-by-Step Guide\nMeta Description: Learn how to solve the algebraic perimeter problem ( 2(w + 3w) = 96 )" step by step, with verification, real-world applications, and key lessons.\nKeywords: perimeter equation, solve 2(w + 3w) = 96, rectangle perimeter formula, algebra word problem, geometry application"]
