Le périmètre est donné par 2(w + 2w) = 36 cm, ce qui se simplifie en 6w = 36 cm.
["Title: How to Solve Linear Equations: Understanding Le Périmètre with 2(w + 2w) = 36 cm", "When solving geometry problems involving perimeters, one of the most common approaches is to translate geometric formulas into algebraic equations. A classic example in French math education is the problem:", "Le périmètre est donné par 2(w + 2w) = 36 cm, ce qui se simplifie en 6w = 36 cm.", "This simple equation forms the foundation for understanding how to calculate the perimeter of rectangular shapes—and how to solve for unknown dimensions using basic algebra.", "---", "### What Does the Equation Mean?", "In any rectangle, the perimeter—the total distance around the shape—is the sum of all four sides. Since opposite sides are equal, a rectangle with width w and length 2w has:", "- Two widths: each measuring w\n- Two lengths: each measuring 2w", "Thus, the perimeter can be expressed as:", "[\n\ ext{Perimeter} = w + w + 2w + 2w = 2w + 2w + 2w + 2w = 2(w + 2w)\n]", "The problem tells us this total perimeter equals 36 cm, leading to the equation:", "[\n2(w + 2w) = 36\n]", "---", "### Step-by-Step Simplification", "Let’s simplify the equation step-by-step to make it easy to solve:", "1. Combine like terms inside the parentheses:", "[\nw + 2w = 3w\n]", "So the equation becomes:", "[\n2(3w) = 36\n]", "2. Multiply:", "[\n6w = 36\n]", "This final simplified form, 6w = 36, is easy to solve.", "---", "### Solving for w", "To find the value of w, divide both sides by 6:", "[\nw = \frac{36}{6} = 6\n]", "So, the width w = 6 cm, and since the length is 2w, it equals:", "[\n2 \ imes 6 = 12 \ ext{ cm}\n]", "---", "### Verifying the Solution", "It’s always good practice to check the result by plugging back into the original perimeter formula:", "[\n\ ext{Perimeter} = 2(w + 2w) = 2(6 + 12) = 2 \ imes 18 = 36 \ ext{ cm}\n]", "The calculation matches, confirming the solution is correct.", "---", "### Why This Matters: Real-World Applications", "Understanding how to set up and solve equations like 2(w + 2w) = 36 cm is essential not only in math class but also in everyday life. Whether you’re determining fencing requirements, designing a garden bed, or calculating materials for construction, perimeter formulas combined with algebraic simplification provide a powerful toolset.", "---", "### Final Thoughts", "The equation 2(w + 2w) = 36 cm perfectly illustrates how geometry and algebra connect. By simplifying expressions, isolating variables, and verifying solutions, we develop critical problem-solving skills. With practice, these basic steps become second nature—empowering you to tackle more complex math challenges with confidence.", "---", "Keywords for SEO:\nle périmètre, calcul de périmètre, équation linéaire, résolution d’équations, géométrie scolaire, simplification d’expression, application mathématique, formule périmètre rectangle, méthode algèbre, mathématiques faciles", "Meta Description:\nDécouvrez comment résoudre facilement le périmètre d’un rectangle avec l’équation 2(w + 2w) = 36 cm. Apprenez pas à pas comment simplifier, isoler la variable et vérifier la solution dans un contexte géométrique.", "---", "Feel free to share this guide with students, teachers, or math enthusiasts learning how algebraic expressions model real-world shapes!"]
