The perimeter is given by \( 2(w + 2w) = 6w = 24 \).
["# How to Calculate the Perimeter: Solving ( 2(w + 2w) = 6w = 24 )", "Understanding how to calculate the perimeter of a rectangle is a fundamental skill in geometry. Whether you're working on homework, designing a room layout, or planning a garden, knowing the perimeter helps with measurements and material estimates. In this article, we’ll walk through the problem ( 2(w + 2w) = 6w = 24 ) step-by-step to find the width ( w ) and the full perimeter.", "## What is Perimeter?", "The perimeter is the total distance around the outside of a geometric shape. For a rectangle, the perimeter formula is:", "[\n\ ext{Perimeter} = 2 \ imes (\ ext{length} + \ ext{width})\n]", "If one side is denoted as ( w ) (the width), then the adjacent side—common in rectangles—is ( 2w ), as given here. This assumption simplifies the perimeter formula to ( 2(w + 2w) ).", "## Step-by-Step Solution", "### Step 1: Simplify the expression inside the parentheses", "Given:\n[ 2(w + 2w) = 24 ]", "First, simplify ( w + 2w ):", "[\nw + 2w = 3w\n]", "Now the equation becomes:", "[\n2(3w) = 24\n]", "### Step 2: Multiply the terms", "[\n6w = 24\n]", "### Step 3: Solve for ( w )", "Divide both sides by 6:", "[\nw = \frac{24}{6} = 4\n]", "So, the width ( w ) is 4 units.", "### Step 4: Find the perimeter", "Recall the perimeter formula ( 2(w + 2w) = 6w ). We already know ( w = 4 ), so:", "[\n6w = 6 \ imes 4 = 24\n]", "Alternatively, using the full expression:", "[\n2(w + 2w) = 2(4 + 8) = 2(12) = 24\n]", "Both ways confirm the perimeter is 24 units.", "## Why This Formulation Matters", "Using ( w + 2w ) reflects how rectangle sides relate—using one dimension (width) and its doubled length—to accurately capture perimeter. This simplification is key in solving real-world problems efficiently.", "## Real-World Applications", "- Interior décor: Calculate how much molding or baseboard is needed around a room\n- Fencing: Determine the total length of fence required for a symmetrical garden bed\n- Construction: Estimate edge materials like baseboards, trim, or edging for outdoor spaces", "## Summary", "Given the equation ( 2(w + 2w) = 6w = 24 ), solving for ( w ) yields ( w = 4 ), and the perimeter is confirmed to be 24 units. This method leverages clear algebraic steps and geometry principles to simplify perimeter calculations for rectangles.", "---", "Keywords: perimeter formula, rectangle perimeter, how to calculate perimeter, solving 2(w + 2w) = 6w, algebra problem, geometry practice, practical math examples, perimeter calculation steps", "---", "Understanding and applying this logic empowers you to tackle similar geometry problems with confidence—whether in textbooks, real life, or advanced math courses."]
