Perimeter = \( 2(w + 2w) = 36 \)
["Perimeter = 2(w + 2w) = 36: A Step-by-Step Guide to Solve the Equation", "Understanding how to calculate the perimeter of a rectangle is a fundamental skill in geometry, essential for students, architects, and DIY enthusiasts alike. One common expression for the perimeter involves simplifying algebraic expressions — like solving Perimeter = 2(w + 2w) = 36 — and using it to find the width w.", "### What Is Perimeter in a Rectangle?", "The perimeter of a rectangle is the total distance around its edges. For a rectangle with width w and length 2w, the formula for perimeter is:", "[\n\ ext{Perimeter} = 2 \ imes (\ ext{length} + \ ext{width}) = 2(w + 2w)\n]", "### Step 1: Simplify the Expression", "Start with the given equation:", "[\n2(w + 2w) = 36\n]", "Simplify inside the parentheses:", "[\nw + 2w = 3w\n]", "Now the equation becomes:", "[\n2(3w) = 36\n]", "### Step 2: Multiply and Solve", "Multiply:", "[\n6w = 36\n]", "Now divide both sides by 6:", "[\nw = \frac{36}{6} = 6\n]", "### Step 3: Interpret the Result", "The width w is 6 units. Since the length is 2w, that equals 12 units. The perimeter equals 36 units, confirming:", "[\n2(6 + 12) = 2 \ imes 18 = 36\n]", "### Why This Equation Matters", "Solving Perimeter = 2(w + 2w) = 36 helps reinforce:", "- How to simplify algebraic expressions\n- The relationship between dimensions and perimeter\n- Real-world applications like fencing a garden, designing rooms, or crafting", "### Final Answer", "[\n\boxed{w = 6}\n]", "This simple algebraic solution shows how combining geometry with basic math enables precise and efficient problem-solving — perfect for both classroom learning and practical use!", "---", "Keywords: Perimeter formula, solving algebra, rectangle dimensions, 2(w + 2w) = 36, geometry, algebra tutorial, solving equations, perimeter calculation, find width, geometry problems.", "Meta Description: Learn how to solve Perimeter = 2(w + 2w) = 36 step-by-step. Understand the algebraic derivation and real-world application in calculating rectangular perimeters."]
