Longueur \( l = 2w = rac{200}{3} \).

["# Solving Longueur ( l = 2w ) and ( l = \frac{200}{3} ): A Step-by-Step Guide", "When dealing with linear equations involving geometric dimensions, clarity and correctness are essential. One useful problem in algebra and applied geometry is solving for length constraints, such as the relationship ( l = 2w ) coupled with the expression ( l = \frac{200}{3} ). This article explores how to solve for width ( w ) and length ( l ) using basic algebraic principles, making it ideal for both educational purposes and quick reference.", "---", "## Understanding the Problem", "We are given two key equations:", "1. ( l = 2w )\n2. ( l = \frac{200}{3} )", "Our task is to determine the values of ( l ) (length) and ( w ) (width). This system represents a simple but essential linear relationship often seen in architectural design, engineering, or manufacturing where proportional scaling matters.", "---", "## Step-by-Step Solution", "### Step 1: Substitute the Expression for ( l )", "Since ( l = 2w ), we can substitute this expression into the second equation:", "[\n2w = \frac{200}{3}\n]", "### Step 2: Solve for Width ( w )", "Divide both sides by 2:", "[\nw = \frac{200}{3} \div 2 = \frac{200}{3} \ imes \frac{1}{2} = \frac{200}{6} = \frac{100}{3}\n]", "So, ( w = \frac{100}{3} ) feet (or meters, depending on unit).", "### Step 3: Solve for Length ( l )", "Now substitute ( w = \frac{100}{3} ) into ( l = 2w ):", "[\nl = 2 \ imes \frac{100}{3} = \frac{200}{3}\n]", "This confirms the given value for length.", "---", "## Final Result", "- Width:\n [\n w = \frac{100}{3} \approx 33.33 \ ext{ units}\n ]", "- Length:\n [\n l = \frac{200}{3} \approx 66.67 \ ext{ units}\n ]", "These values satisfy both constraints: the length is exactly twice the width, and the length equals ( \frac{200}{3} ).", "---", "## Why This Equation Matters", "This type of linear relationship commonly appears in:", "- Proportional design, where length scales directly with width\n- Manufacturing tolerances, ensuring uniform dimensions\n- Geometric constraints, such as designing rectangles with fixed aspect ratio and one known perimeter or diagonal", "Using the equation ( l = 2w ) simplifies complex spatial reasoning into clean algebraic form—efficient and reliable.", "---", "## Tips for Quick Application", "- Always substitute one equation into the other to reduce variables\n- Remember that this is a system of linear equations in one variable\n- Cross-check units for consistency—here all lengths are expressed in the same unit\n- For real-world scaling, multiply or divide whole numbers by 3 to avoid decimals", "---", "## Conclusion", "The equation ( l = 2w ) combined with ( l = \frac{200}{3} ) exemplifies how algebra streamlines geometric problem-solving. With simple substitution, we find ( w = \frac{100}{3} ) and ( l = \frac{200}{3} )—a perfect match. Whether in math classrooms or engineering workflows, mastering such linear relationships is key to connecting dimension and dimension logic.", "---", "Keywords: longueur ( l = 2w ), solve for width and length, linear equations geometry, algebra linear system, ( l = \frac{200}{3} ), proportional design, mathematical reasoning, practical algebra, mathematical equations applied", "Meta description: Solve ( l = 2w ) and ( l = \frac{200}{3} ) using substitution. Step-by-step guide to find width ( w = \frac{100}{3} ) and length ( l = \frac{200}{3} ), ideal for math students and professionals."]