The perimeter \( P = 2(l + w) = 2(3w + w) = 8w = 64 \).
["Title: How to Calculate the Perimeter of a Rectangle: Step-by-Step Example with ( P = 64 )", "Understanding the perimeter of a rectangle is a fundamental concept in geometry—essential for fields like architecture, landscaping, and construction. In this article, we’ll explore how to find the perimeter using the formula ( P = 2(l + w) ), with a specific example where ( l = 3w ) and the perimeter ( P = 64 ).", "---", "### Understanding the Perimeter Formula", "The perimeter ( P ) of a rectangle is calculated using the formula:", "[\nP = 2(l + w)\n]", "where:\n- ( l ) = length of the rectangle\n- ( w ) = width of the rectangle", "This formula works because a rectangle has two lengths and two widths, adding up to one full loop around the shape.", "---", "### Applying the Formula with Given Values", "Let’s apply the formula to the case where:\n- The length ( l = 3w )\n- The perimeter ( P = 64 )", "Substitute these values into the perimeter equation:", "[\n64 = 2(l + w) = 2(3w + w)\n]", "Simplify the expression inside the parentheses:", "[\n64 = 2(4w)\n]", "[\n64 = 8w\n]", "Now, solve for ( w ):", "[\nw = \frac{64}{8} = 8\n]", "So, the width is ( 8 ) units.", "---", "### Calculate the Length", "Since ( l = 3w ), substitute ( w = 8 ):", "[\nl = 3 \ imes 8 = 24\n]", "---", "### Verify the Perimeter", "Let’s double-check by plugging ( l = 24 ) and ( w = 8 ) back into the perimeter formula:", "[\nP = 2(l + w) = 2(24 + 8) = 2 \ imes 32 = 64\n]", "The calculation confirms that the perimeter is indeed ( 64 ), matching the given value.", "---", "### Key Takeaways", "- The perimeter formula ( P = 2(l + w) ) efficiently combines length and width to compute the total distance around the rectangle.\n- When one side is a multiple of the other (e.g., length = 3 × width), substitution simplifies the equation.\n- Solving step-by-step ensures accuracy and reinforces algebra skills.\n- Confirming results by plugging values back into the formula validates correctness.", "---", "### Real-World Applications", "Knowing how to calculate perimeter helps in countless real-life scenarios such as:\n- Determining how much fencing is needed for a garden bed\n- Calculating materials for building a rectangular room’s border\n- Planning landscaping designs with uniform edges", "---", "Conclusion\nBy breaking down the perimeter formula and substituting known relationships, even complex perimeter problems become manageable. Whether you’re a student mastering geometry or a professional solving design challenges, mastering perimeter calculations like ( P = 2(l + w) ) starts with clear steps and practice.", "---", "Keywords: perimeter formula, rectangle perimeter, P = 2(l + w), calculating perimeter, L = 3w, fencing perimeter example, geometry basics.\nMeta Description: Learn how to calculate the perimeter of a rectangle using the formula ( P = 2(l + w) ), with a step-by-step example where ( P = 64 ), length ( l = 3w ).", "---", "Need more geometry help? Explore our guides on area calculations, diagonal of rectangles, and perimeter problems with integer solutions."]
