Let the width be \( w \). Then the length is \( 3w \). The perimeter \( P \) of a rectangle is given by:

["Title: Rectangle Dimensions Recap: Width ( w ), Length ( 3w ), and Perimeter Explained", "When studying geometry, understanding the relationship between a rectangle’s width, length, and perimeter is fundamental. This article breaks down how width ( w ) and length ( 3w ) define the rectangle’s perimeter ( P )—a key concept for students and enthusiasts alike.", "---", "### Understanding the Rectangle Formula", "A rectangle’s perimeter ( P ) is the total distance around its edges. The formula for the perimeter of any rectangle is:\n[\nP = 2 \ imes (\ ext{length} + \ ext{width})\n]", "Given here:\n- Width = ( w )\n- Length = ( 3w )", "---", "### Plugging in the Values", "Substitute width and length into the perimeter formula:\n[\nP = 2 \ imes (3w + w)\n]", "Combine the terms inside the parentheses:\n[\nP = 2 \ imes (4w)\n]", "---", "### Simplifying the Expression", "Now multiply:\n[\nP = 8w\n]", "---", "### Final Result", "Thus, if the width of a rectangle is ( w ) and the length is ( 3w ), its perimeter is:\n( P = 8w )", "This clear relationship makes it easy to calculate perimeter anytime the width is known—an essential tool in architecture, landscaping, and everyday problem-solving.", "---", "### Key Takeaways", "- The perimeter formula ( P = 2(l + w) ) applies universally.\n- For rectangles with length ( 3w ) and width ( w ), perimeter simplifies neatly to ( 8w ).\n- Understanding these formulas strengthens spatial reasoning and algebraic skills.", "Whether in math class or real-world applications, knowing how dimensions translate to perimeter helps make accurate measurements and efficient designs—proof that even simple geometric principles unlock powerful practical knowledge.", "---", "Try it yourself: Suppose ( w = 5 ). What is the perimeter?\n[\nP = 8 \ imes 5 = 40\n]\nCheck: length = 15, width = 5, ( P = 2(15 + 5) = 2 \ imes 20 = 40 )—confirmed!", "---", "### Optimize Your Learning\n- Use the formula to explore other rectangles by changing ( w ).\n- Apply perimeter results in projects like fencing, tiling, or design sketches.\n- Master this equation to build confidence in geometry and algebra.", "---", "Keywords: rectangle perimeter, length ( 3w ), width ( w ), formula ( P = 8w ), geometry tutorial, math tips, educational formula, perimeter calculation", "---", "Meta Description:\nLearn how to calculate the perimeter of a rectangle with width ( w ) and length ( 3w ) using the formula ( P = 8w ). Understand the derivation and apply it to real-world problems. Ideal for students and geometry learners."]