The perimeter is \( 2(x + 2x) = 36 \).
["### Solving the Perimeter Equation: Understanding ( 2(x + 2x) = 36 )", "When tackling geometry problems involving perimeters, understanding how to simplify and solve equations is essential. One classic example is finding ( x ) in the equation:", "[\n2(x + 2x) = 36\n]", "This equation frequently appears in geometry and algebra contexts, especially when calculating the perimeter of shapes where side lengths are expressed in terms of a variable.", "---", "### Breaking Down the Equation", "Start by simplifying the expression inside the parentheses:", "[\nx + 2x = 3x\n]", "Substitute back:", "[\n2(3x) = 36\n]", "This simplifies to:", "[\n6x = 36\n]", "---", "### Solving for ( x )", "To isolate ( x ), divide both sides by 6:", "[\nx = \frac{36}{6} = 6\n]", "---", "### Practical Application: Finding the Perimeter", "Suppose this equation models the perimeter of a rectangle. If one side measures ( x ) and the adjacent side is ( 2x ), then the total perimeter—defined as the sum of all sides—is expressed as ( 2(x + 2x) ). Given the perimeter equals 36 units, we now know:", "- ( x = 6 ), so one side is 6 units\n- The other side is ( 2x = 12 ) units\n- Perimeter: ( 2(6 + 12) = 2 \ imes 18 = 36 ) units — confirming the solution", "This method applies broadly in real-world geometry, helping students and professionals alike solve for unknown dimensions when shape properties are expressed algebraically.", "---", "### Key Takeaways", "- Simplify inner expressions carefully before multiplying.\n- Always verify units and dimensions in real-world applications.\n- Solving perimeter-based equations helps reinforce algebraic and geometric reasoning.", "---", "### Final Answer Summary", "[\n2(x + 2x) = 36 \quad \Rightarrow \quad 6x = 36 \quad \Rightarrow \quad x = 6\n]", "This confirms the side lengths based on geometric properties and algebraic manipulation.", "---", "Keywords: perimeter equation, solve 2(x + 2x) = 36, algebra geometry, perimeter calculation, algebra basics, step-by-step perimeter problem", "Learn how simplifying expressions leads to solving real-world geometry problems efficiently!"]
