A rectangle has a perimeter of 50 meters and a length that is twice its width. What are the dimensions of the rectangle?
["Rectangle Dimensions: How to Calculate Length and Width When Perimeter and Length Relationship Are Known", "Understanding the dimensions of a rectangle using basic geometric formulas is essential for students, DIY enthusiasts, and professionals alike. One common problem involves a rectangle with a perimeter of 50 meters and a length that is twice its width. This practical example makes it easy to grasp how algebra and geometry connect in real-world applications.", "### Given:\n- Perimeter (P) = 50 meters\n- Length (L) = 2 × Width (W)", "### Step-by-Step Calculation:", "The formula for the perimeter of a rectangle is:", "[\nP = 2 \ imes (L + W)\n]", "Substitute the known values into the equation:", "[\n50 = 2 \ imes (L + W)\n]", "Now, replace L with 2W since the length is twice the width:", "[\n50 = 2 \ imes (2W + W)\n]", "[\n50 = 2 \ imes 3W\n]", "[\n50 = 6W\n]", "Now, solve for W:", "[\nW = \frac{50}{6} = \frac{25}{3} \approx 8.33 \ ext{ meters}\n]", "Now calculate the length:", "[\nL = 2W = 2 \ imes \frac{25}{3} = \frac{50}{3} \approx 16.67 \ ext{ meters}\n]", "### Final Answer:\n- Width = ( \frac{25}{3} ) meters (≈ 8.33 m)\n- Length = ( \frac{50}{3} ) meters (≈ 16.67 m)", "### Why This Matters:\nThis method can help you determine unknown dimensions in construction, landscaping, fencing, or design projects. Knowing how to apply the perimeter formula with a given length-width relationship saves time and ensures accuracy.", "### Key Takeaway:\nGiven a rectangle’s perimeter and a proportional relationship between length and width, substitute variables wisely, solve step-by-step using algebra, and verify your results to find clean, accurate dimensions.", "---", "If you're regularly solving rectangle problems, practice these steps to build speed and confidence. Whether you're drawing blueprints or calculating materials, mastering this approach ensures you never overlook essential geometry!"]
