Périmètre = 2(w + 2w) = 2(3w) = 6w = 36 → w = 6 cm
["How to Solve Linear Equations Like Périmètre = 2(w + 2w) = 6w = 36: Finding the Value of w (6 cm)", "Understanding how to solve basic algebraic equations is essential for mastering geometry—and one common problem involves finding the unknown dimension based on perimeter. Today, we explore a straightforward equation based on the perimeter of a rectangle, using Périmètre = 2(w + 2w) = 6w = 36, and find that w = 6 cm. This step-by-step guide helps clarify how algebraic reasoning simplifies geometric problems.", "---", "### What Is the Périmètre and Why Does It Matter?", "In geometry, the périmètre (perimeter) is the total length around a shape. For a rectangle, the perimeter is calculated as:\nPérimètre = 2 × (longueur + largeur)\nGiven the problem Périmètre = 2(w + 2w) = 6w, and Périmètre = 36 cm, we solve for the width w.", "---", "### Step-by-Step Solution", "1. Start with the given formula:\n [\n Périmètre = 2(w + 2w)\n ]\n Simplify inside the parentheses:\n [\n Périmètre = 2(3w)\n ]", "2. Multiply to find simplified form:\n [\n Périmètre = 6w\n ]", "3. Set equal to the known perimeter:\n [\n 6w = 36\n ]", "4. Solve for w by dividing both sides by 6:\n [\n w = \frac{36}{6} = 6\n ]", "Thus, the width w = 6 cm.", "---", "### The Width of the Rectangle", "Using w = 6 cm, the length (2w) is:\n[\n2w = 2 × 6 = 12 \ ext{ cm}\n]\nSo the rectangle has a width of 6 cm and a length of 12 cm, confirming:\n[\n\ ext{Périmètre} = 2 × (6 + 12) = 2 × 18 = 36 \ ext{ cm}\n]\nThis matches the problem statement exactly.", "---", "### Practical Takeaways", "- Simplifying expressions like Périmètre = 2(w + 2w) helps reduce complex formulas algebraically.\n- Recognizing that w + 2w = 3w allows quick simplification to 6w in this case.\n- Solving linear equations such as 6w = 36 is fast when you isolate w by division.", "This approach is valuable not only in geometry but any math or real-world context involving unknown dimensions. Whether calculating materials for a project or solving for variables, these algebraic skills build a strong foundation.", "---", "### Summary", "- The perimeter formula reduces to 6w\n- Given Périmètre = 36, solving 6w = 36 gives w = 6 cm\n- Width = 6 cm, Length = 12 cm, Perimeter checks out\n- Straightforward algebra empowers quick and accurate problem-solving", "For students and learners, mastering this pattern strengthens problem-solving confidence and paves the way for more advanced math.", "---", "Keywords:\nperimetre calcul, résoudre équation linéaire, calcul géométrie, périmètre rectangle, w = 6 cm, résolution algèbre terme simple, périmètre rectangle 36 cm", "---\nUnderstanding Périmètre = 2(w + 2w) = 6w = 36 solves directly to w = 6 cm — a key step in linking algebra with geometric shapes."]
