Le périmètre \( P = 2l + 2w = 2(2w) + 2w = 6w \).

["Title: Understanding Le Périmètre d’un Rectangle : Formule, Calcul et Application Pratique", "---", "### Introduction", "When studying geometry, one of the most fundamental concepts is the perimeter of a rectangle. Whether you’re designing a garden, laying tiles, or solving a math problem, knowing how to calculate the perimeter efficiently is essential. This article explores the perimeter formula for a rectangle—specifically ( P = 2l + 2w )—with a detailed focus on the case when width ( w = 2w ), simplifying it to ( P = 6w ). We’ll break down each step to help students, teachers, and DIY enthusiasts master this concept effortlessly.", "---", "### What Is the Perimeter of a Rectangle?", "The perimeter is the total distance around the outside of a two-dimensional shape. For a rectangle, it represents the sum of the lengths of all four sides. Since opposite sides of a rectangle are equal—two sides have length ( l ) and two sides have width ( w )—the perimeter formula simplifies elegantly:", "[\nP = 2l + 2w\n]", "This means you add the lengths of the length (( l )) and width (( w )), then multiply by 2.", "---", "### How to Simplify: When ( l = 2w )", "In many real-world situations, the length may be defined in relation to the width. For example, if ( l = 2w ), we substitute this relationship directly into the perimeter formula:", "[\nP = 2l + 2w = 2(2w) + 2w\n]", "Now simplify:", "[\nP = 4w + 2w = 6w\n]", "So, the perimeter of the rectangle becomes ( P = 6w ), revealing that the perimeter depends only on the width when length is twice the width.", "---", "### Why This Simplification Matters", "Expressing the perimeter as ( 6w ) is more efficient than keeping it as ( 2(2w) + 2w ), especially in algebra, optimization problems, or when adjusting dimensions. This simplified form clearly shows how perimeter scales with width, making it easier to visualize and calculate changes—such as doubling the width or adjusting tile placement.", "---", "### Practical Applications of Rectangle Perimeter", "Understanding the perimeter formula has countless practical uses:", "- Interior design & decorating: Calculating the length of baseboards, crown molding, or rugs.\n- Construction & renovation: Measuring fencing, roofing materials, or flooring.\n- Gardening: Determining the length of garden beds or fence posts.\n- Education: Teaching students about geometric relationships and algebraic expressions.", "---", "### Step-by-Step Summary", "To calculate the perimeter when ( l = 2w ):", "1. Start with the perimeter formula:\n ( P = 2l + 2w )\n2. Substitute ( l = 2w ):\n ( P = 2(2w) + 2w )\n3. Multiply:\n ( P = 4w + 2w )\n4. Combine like terms:\n ( P = 6w )", "Thus, the perimeter is directly proportional to the width, simplifying both calculations and design planning.", "---", "### Conclusion", "Mastering the perimeter formula ( P = 2l + 2w )—and especially simplifying it when ( l = 2w )—empowers you to solve geometry problems quickly and accurately. The simplified expression ( P = 6w ) highlights the intimate relationship between length and width in rectangular shapes, supporting everything from homework assignments to real-life projects. Whether you’re building a deck or studying for a math exam, knowing how to compute perimeter efficiently is an invaluable skill.", "---", "### Keywords for SEO Optimization", "- Périmètre rectangle\n- Périmètre calcul simple\n- Formule périmètre rectangle\n- Périmètre = 2l + 2w\n- Simplification périmètre rectangle\n- Rectangle perimeter formula\n- Calculaire périmètre facile\n- Perimeter rectangle simplified\n- Géométrie élémentaire\n- Diagonal et périmètre rectangle", "---", "Ready to calculate your rectangle’s perimeter in seconds? Use ( P = 6w ) when the length is twice the width and simplify your workflow today!", "---", "Stay tuned for more geometry tips to make math clear, easy, and practical!"]