Use the perimeter formula: \( 2(w + 2w) = 36 \)

["Using the Perimeter Formula: How to Solve ( 2(w + 2w) = 36 )", "Understanding the perimeter formula is essential for solving geometry problems involving rectangles—especially when working with repetitive or scaled dimensions. One straightforward and frequently used example is solving ( 2(w + 2w) = 36 ), where ( w ) represents the width of a rectangular figure and ( 2w ) is its length (twice the width).", "### What is the Perimeter of a Rectangle?", "The perimeter ( P ) of a rectangle is calculated using the formula:\n[\nP = 2(\ ext{length} + \ ext{width})\n]\nSince length and width are added and multiplied by 2, the formula simplifies to:\n[\nP = 2(w + 2w)\n]\nHere, ( w ) is width and ( 2w ) is length.", "### Solving the Equation ( 2(w + 2w) = 36 )", "Step 1: Simplify inside the parentheses.\n[\nw + 2w = 3w\n]\nSo the equation becomes:\n[\n2(3w) = 36\n]", "Step 2: Multiply inside the parentheses.\n[\n6w = 36\n]", "Step 3: Divide both sides by 6 to solve for ( w ).\n[\nw = \frac{36}{6} = 6\n]", "### Conclusion: Dimensions and Final Answer", "The width ( w ) is 6 units. Since the length is ( 2w ):\n[\n\ ext{Length} = 2 \ imes 6 = 12 \ ext{ units}\n]", "The perimeter is confirmed as:\n[\n2(6 + 12) = 2 \ imes 18 = 36 \ ext{ units}\n]", "This example demonstrates how the perimeter formula helps efficiently determine missing dimensions when the total perimeter is known—especially useful in real-world applications like fencing, construction, and design. Always simplify expressions carefully and remember: perimeter = twice the sum of length and width.", "Keywords: perimeter formula, solve 2(w + 2w) = 36, geometry lesson, rectangular perimeter, algebra practice, rectangle problems, solve perimeter equation, math tutorial."]