The perimeter is given by \( 2(x + 2x) = 60 \).
["Understanding the Perimeter Formula: Solving ( 2(x + 2x) = 60 )", "When solving geometry problems involving perimeter, one of the most common expressions you’ll encounter is the perimeter of a rectangular shape, often written as ( 2 \ imes (\ ext{length} + \ ext{width}) ). In this case, the given equation ( 2(x + 2x) = 60 ) helps us determine the value of ( x ), which represents key dimensions of a rectangle, such as length and width.", "### Breaking Down the Equation", "The perimeter formula for a rectangle is derived from the fact that a rectangle has two pairs of equal sides. If one side is ( x ) and the adjacent side is ( 2x ), the perimeter is calculated as:", "[\n\ ext{Perimeter} = 2(\ ext{length} + \ ext{width}) = 2(x + 2x)\n]", "Simplify the expression inside the parentheses:", "[\nx + 2x = 3x\n]", "Thus, the perimeter equation becomes:", "[\n2(3x) = 60\n]", "Which simplifies further to:", "[\n6x = 60\n]", "### Solving for ( x )", "To find ( x ), divide both sides by 6:", "[\nx = \frac{60}{6} = 10\n]", "### Determining the Actual Dimensions", "Now that we know ( x = 10 ), substitute back to find the actual side lengths:", "- Width = ( x = 10 ) units\n- Length = ( 2x = 20 ) units", "This confirms the sides are in a standard ratio: 20 and 10, making the rectangle dimensions easy to work with.", "### Why This Perimeter Equation Matters", "Understanding how to derive and solve equations like ( 2(x + 2x) = 60 ) is essential in geometry for problems involving fencing, land measurement, or construction planning. It teaches the fundamental relationship between shape variables and measurable parameters like perimeter.", "### Step-by-Step Summary:", "| Step | Equation / Action | Result |\n|---------------------|----------------------------------------|-------------------------|\n| Original expression | ( 2(x + 2x) = 60 ) | |\n| Simplify inside | ( x + 2x = 3x ) | |\n| Perimeter formula | ( 2(3x) = 60 ) | |\n| Solve for ( x ) | ( 6x = 60 \Rightarrow x = 10 ) | |\n| Side lengths | Width = ( 10 ), Length = ( 20 ) | |", "### Final Thoughts", "Mastering perimeter equations not only helps with math exams but also builds critical reasoning skills applicable in real-world scenarios. Whether planning a garden or designing a room, knowing how to translate geometric formulas into solved values is indispensable. The equation ( 2(x + 2x) = 60 ) offers a clear, straightforward example of perimeter calculation and problem-solving in algebra and geometry.", "---", "Keywords: perimeter equation, 2(x + 2x) = 60, rectangular perimeter, solve for x, geometry tutorial, algebra fundamentals, perimeter calculation, linear equation, length and width, solving perimeter problems."]
