A rectangle's length is twice its width. If the perimeter is 60 meters, what are the dimensions of the rectangle?
["Title: How to Calculate the Dimensions of a Rectangle When Length is Twice the Width – A 60-Meter Perimeter Case", "When solving geometry problems, one common scenario involves rectangles where the length is twice the width and the perimeter is given—perfect for deeper understanding of algebraic modeling. If a rectangle’s length equals twice its width, and its perimeter measures 60 meters, determining its exact dimensions becomes a straightforward yet insightful exercise.", "### Understanding the Problem", "Let’s define the rectangle’s dimensions clearly:\n- Let the width = w meters\n- Then the length = 2w meters (since it’s twice the width)", "The perimeter P of a rectangle is calculated using the formula:\n[ P = 2 \ imes (\ ext{length} + \ ext{width}) ]\nSubstituting the known values:\n[ 60 = 2 \ imes (2w + w) ]", "### Step-by-Step Calculation", "1. Simplify the expression inside the parentheses:\n[ 60 = 2 \ imes (3w) ]\n[ 60 = 6w ]", "2. Solve for width:\n[ w = \frac{60}{6} = 10 \ ext{ meters} ]", "3. Find the length using the relationship (length = 2 × width):\n[ \ ext{Length} = 2w = 2 \ imes 10 = 20 \ ext{ meters} ]", "### Final Dimensions", "- Width = 10 meters\n- Length = 20 meters", "### Why This Formula Works", "This method leverages algebraic expressions derived from geometric properties. By expressing all measurements in terms of one variable (width), you convert a real-world measurement problem into a solvable equation. The simplicity of rectangles and the linear relationship between length and width make them ideal for teaching and applying basic algebra.", "---", "### Summary", "- A rectangle with length twice the width and a perimeter of 60 meters has:\n - Width = 10 meters\n - Length = 20 meters \nThis clear, step-by-step approach helps students and enthusiasts alike master essential perimeter and dimension calculations while reinforcing algebraic thinking.", "Key Takeaway: Always define variables based on problem relationships—like width first—and use the perimeter formula to solve efficiently.", "---", "Keywords: rectangle dimensions, length twice width, perimeter formula, algebra geometry, rectangle calculator, 60 meter perimeter, solve geometry problems, algebra basics, width and length relation"]
