The perimeter is given by \( 2(w + 3w) = 64 \).
["# How to Solve "The Perimeter is Given by ( 2(w + 3w) = 64 )" – Step-by-Step Guide", "Understanding the perimeter formula is essential in geometry, and solving equations like ( 2(w + 3w) = 64 ) is a common problem in algebra and basic geometry. This article walks you through simplifying and solving this equation clearly and effectively — perfect for students learning geometry fundamentals or preparing for standardized tests.", "---", "## What is Perimeter and Why Does It Matter?", "Perimeter refers to the total distance around the outside of a two-dimensional shape. For rectangles, the perimeter formula is:", "[\n\ ext{Perimeter} = 2 \ imes (\ ext{Length} + \ ext{Width})\n]", "In this problem, we are told that the perimeter is described by the equation:", "[\n2(w + 3w) = 64\n]", "Here, the width is ( w ) and the length is ( 3w ), a typical relationship in problems involving linear dimensions.", "---", "## Step-by-Step Solution: How to Solve ( 2(w + 3w) = 64 )", "Step 1: Simplify the Expression Inside the Parentheses", "Start by combining like terms inside the parentheses:", "[\nw + 3w = 4w\n]", "Now the equation becomes:", "[\n2(4w) = 64\n]", "Step 2: Multiply", "Multiply 2 by 4w:", "[\n8w = 64\n]", "Step 3: Solve for ( w )", "Divide both sides of the equation by 8:", "[\nw = \frac{64}{8} = 8\n]", "---", "## Final Answer", "The width ( w = 8 ). Since the length is ( 3w ):", "[\n\ ext{Length} = 3 \ imes 8 = 24\n]", "Perimeter = ( 2 \ imes (8 + 24) = 2 \ imes 32 = 64 ), which confirms the given equation.", "---", "## Why This Method Works", "- Combining like terms simplifies the expression and clarifies the relationship between variables.\n- Clear algebraic steps ensure accuracy and help avoid common mistakes.\n- Verifying the solution by plugging it back into the perimeter formula confirms correctness.", "---", "## Tips for Mastering Perimeter Problems", "- Always identify length and width clearly before substituting into formulas.\n- Simplify inside parentheses before multiplying.\n- Double-check your work by substituting your solution back into the original equation.\n- Recognize standard relationships like “length is three times the width” and apply them accurately.", "---", "## Conclusion", "Solving ( 2(w + 3w) = 64 ) is a straightforward but powerful exercise in applying the perimeter formula with algebra. By simplifying step-by-step and verifying your result, you ensure both accuracy and deeper understanding — key skills in mastering geometry and algebra.", "Whether you're a student tackling homework or brushing up on fundamentals, mastering perimeter equations like this helps build confidence and competence in math.", "---", "Keywords: perimeter equation, solving 2(w + 3w) = 64, rectangle perimeter, algebra perimeter, geometry equations, solving linear equations, simplify expressions, math tutorial, perimeter problem steps."]
