El perímetro se da por \( 2(w + 3w) = 64 \).

["Title: Understanding El Perímetro en Términos Algebraicos: La Fórmula ( 2(w + 3w) = 64 )", "---", "Introduction\nLearning to calculate the perimeter of geometric shapes using algebra is a foundational skill in mathematics. A common problem students encounter involves rectangles where one side is expressed in terms of ( w ), such as ( 2(w + 3w) = 64 ). In this article, we’ll explore how to interpret, solve, and apply this equation step-by-step—perfect for mastering algebra and geometry.", "---", "What is Perímetro and Why Use Algebra?\nPerímetro refers to the total distance around a two-dimensional shape. For rectangles, the perimeter formula ( P = 2(\ ext{largo} + \ ext{ancho}) ) applies. When one dimension is unknown, expressing it algebraically—like ( 3w ) as the length—lets us write equations that model real-world scenarios.", "---", "Decoding the Expression: ( 2(w + 3w) = 64 )\nThe equation models a rectangle where:\n- ( w ) = width (one side),\n- ( 3w ) = length (three times the width),\n- ( w + 3w ) = sum of length and width,\n- ( 2(\ ext{sum}) ) = perimeter.", "So, the entire expression calculates the total perimeter and sets it equal to 64.", "---", "Step-by-Step Solution\n1. Simplify inside the parentheses:\n ( w + 3w = 4w )\n This reduces the original equation to:\n [ 2(4w) = 64 ]", "2. Simplify the multiplication:\n ( 2 \cdot 4w = 8w ), so:\n [ 8w = 64 ]", "3. Solve for ( w ):\n Divide both sides by 8:\n [ w = \frac{64}{8} = 8 ]", "---", "Answer: The Width ( w = 8 )\nThus, the width of the rectangle is 8 units, and the length is ( 3w = 24 ) units. The perimeter checks as:\n[ P = 2(8 + 24) = 2(32) = 64 ]\nThis confirms the solution satisfies the original equation.", "---", "Why This Problem Matters\nUnderstanding algebraic expressions like ( 2(w + 3w) = 64 ) helps develop problem-solving skills applicable in architecture, construction, and design—fields relying heavily on precise measurements. It also strengthens the ability to translate word problems into mathematical models.", "---", "Practice Problem\nCan you solve this? If the perimeter of a rectangle is ( 2(w + 4w) = 80 ), what is ( w )?", "---", "Summary\n- Perímetro of a rectangle: ( P = 2(\ ext{largo} + \ ext{ancho}) )\n- Simplify ( w + 3w = 4w ) → ( 2(4w) = 8w )\n- Solve ( 8w = 64 ) → ( w = 8 )\nMastering these steps makes algebraic geometry intuitive—and essential for advanced math and practical applications.", "---", "Keywords:\n- Perímetro algebraico\n- Cómo resolver perímetro\n- Ecuación ( 2(w + 3w) = 64 )\n- Álgebra línea recta\n- Aplicación matemática\n- Matemáticas de secundaria", "---", "Link to Related Topics:\n- Solve linear equations with variables on both sides\n- Perímetro en el mundo real\n- Geometría algebraica para principiantes", "---", "Remember:\nMathematics becomes clear when you break down expressions—whether solving ( 2(w + 3w) = 64 ) or larger problems. Keep practicing, and let algebra guide your understanding!"]