Perimeter: 2(w + 3w) = 64 → 2(4w) = 64 → 8w = 64 → w = 8
["Understanding Perimeter: Solving Perimeter Problems Using Algebra – Solved Step-by-Step", "Calculating the perimeter of a shape is a fundamental concept in geometry, but solving these problems efficiently often involves algebra. One classic example is solving equations like Perimeter: 2(w + 3w) = 64, which simplifies down to finding the width w. In this article, we break down the steps to solve this problem, explaining how to use algebraic techniques effectively. Whether you're a student preparing for exams or someone curious about geometry and algebra, this guide will help clarify the process.", "---", "### What Is Perimeter?", "The perimeter is the total distance around the boundary of a two-dimensional shape. For a rectangle — a common shape in perimeter problems — the perimeter formula is:", "[\n\ ext{Perimeter} = 2 \ imes (\ ext{Length} + \ ext{Width})\n]", "This formula applies because a rectangle has two identical lengths and two identical widths.", "---", "### Solving Perimeter Equations Step-by-Step", "Let’s apply this to the equation:", "[\n2(w + 3w) = 64\n]", "#### Step 1: Simplify inside the parentheses\nInside the parentheses, we combine like terms:", "[\nw + 3w = 4w\n]", "Now the equation becomes:", "[\n2(4w) = 64\n]", "#### Step 2: Multiply\nMultiply 2 by 4w:", "[\n8w = 64\n]", "#### Step 3: Solve for w\nTo isolate w, divide both sides by 8:", "[\nw = \frac{64}{8} = 8\n]", "So, the width w of the rectangle is 8 units.", "---", "### Why This Matter: Real-World Applications\nUnderstanding how to solve for unknown dimensions using perimeter equations is useful in real-world scenarios such as:", "- Construction: Determining material needs based on boundary measurements\n- Garden design: Planning fencing or planting space\n- Interior design: Calculating trim or border lengths\n- Math education: Building foundational algebra skills", "---", "### Pro Tips for Solving Perimeter Problems Algebraically", "1. Simplify expressions first: Always combine like terms inside parentheses.\n2. Follow order of operations: Perform multiplications and divisions before additions or equal signs.\n3. Isolate the variable: Use inverse operations to solve for unknowns.\n4. Check your answer: Substitute w = 8 back into the original equation to verify.", "For instance:\nLeft side: ( 2(8 + 3×8) = 2(8 + 24) = 2×32 = 64 ) ✓\nRight side: 64 — verified!", "---", "### Conclusion", "Solving perimeter equations like 2(w + 3w) = 64 doesn’t have to be difficult. By simplifying expressions, applying basic arithmetic, and isolating variables, even complex-looking problems become manageable. Mastering this technique strengthens algebraic reasoning and prepares you for advanced geometry and real-life applications.", "Next time you see a perimeter equation, take a moment to break it down step by step — you’ll find the solution is often closer than it seems!", "---", "Keywords: perimeter algebra, how to solve perimeter equations, algebraic solution steps, solving 2(w + 3w) = 64, simplify linear equations, geometry algebra, mathematics problem-solving", "Meta Description: Learn how to solve perimeter equations using algebra with step-by-step examples. Solve 2(w + 3w) = 64 in minutes by simplifying, combining like terms, and isolating the variable w. Perfect for students and math learners."]
