The perimeter is \(2(w + 3w) = 64\).

["Title: Solving Perimeter Equations: How to Solve (2(w + 3w) = 64) Step-by-Step", "Understanding geometry fundamentals begins with mastering perimeter calculations—but sometimes algebra gets in the way. One common problem faced by students and math learners is solving equations involving perimeters, such as:", "[\n2(w + 3w) = 64\n]", "This equation appears simple, but it's a perfect example of how combining algebraic expressions and geometry concepts strengthens problem-solving skills. In this article, we’ll break down how to solve (2(w + 3w) = 64) step-by-step, explain what the perimeter represents, and highlight common pitfalls to avoid. Whether you're a student, teacher, or just curious, this guide will clarify this classic perimeter challenge.", "---", "### What Does the Perimeter Equation Represent?", "The perimeter is the total distance around a shape. In this problem, the expression (w + 3w) suggests a rectangular shape where:", "- (w) represents the width of the rectangle.\n- (3w) represents the length—possibly three times the width—typical in problems involving proportional dimensions.", "The full expression (2(w + 3w)) expands to the total perimeter, and setting it equal to 64 means the shape’s boundary length is 64 units. Solving this gives the value of (w), the width, which unlocks the full dimensions of the rectangle.", "---", "### Step-by-Step Solution to (2(w + 3w) = 64)", "Let’s solve the equation step-by-step:", "1. Simplify inside the parentheses:\n (w + 3w = 4w)\n So the equation becomes:\n [\n 2(4w) = 64\n ]", "2. Multiply:\n (2 \ imes 4w = 8w), thus:\n [\n 8w = 64\n ]", "3. Isolate (w):\n Divide both sides by 8:\n [\n w = \frac{64}{8} = 8\n ]", "---", "### Finding the Full Dimensions", "Now that we know:\n- Width (w = 8)\n- Length (3w = 3 \ imes 8 = 24)", "We can verify the perimeter:\n[\n2(w + 3w) = 2(8 + 24) = 2(32) = 64\n]\n✅ The solution checks out!", "---", "### Why Solving Perimeter Equations Matters", "Beyond deriving dimensions, mastering perimeter algebra strengthens your ability to:\n- Translate real-world scenarios into equations.\n- Simplify and manipulate expressions confidently.\n- Apply algebraic thinking to geometry problems.", "Perimeter problems are foundational for architecture, interior design, construction, and even competitive math—making this skill vital for academic and professional success.", "---", "### Common Mistakes to Avoid", "While solving (2(w + 3w) = 64) seems straightforward, learners often stumble on these fronts:\n- Incorrectly combining like terms (e.g., treating (w + 3w) as (4w) without synonymizing).\n- Forgetting to divide both sides by the coefficient after simplification.\n- Mixing up perimeter with area or misassigning variables.\nDouble-check each step and visualize the shape to reduce errors.", "---", "### Final Thoughts", "The equation (2(w + 3w) = 64) is a small but powerful example of how algebra and geometry intersect. By simplifying expressions, solving linear equations, and validating results, you gain clarity on perimeter problems that extend far beyond textbooks.", "Whether you're measuring a room, designing a garden, or conquering math homework, remember—perimeter isn’t just a shape boundary: it’s your gateway to spatial reasoning and critical thinking.", "---", "Keywords for SEO:\nperimeter equation, solve 2(w + 3w) = 64, algebra perimeter problem, rectangular perimeter calculation, step-by-step perimeter solution, solve linear equations, geometry application, equity in math education, perimeter and algebra, solving w + 3w = 64", "Meta Description:\nSolve the perimeter equation (2(w + 3w) = 64) step-by-step. Learn how combining algebra and geometry helps find unknown dimensions. Perfect for students mastering perimeter concepts."]