["# Solve for ( x ): Perimeter Equation ( 2(x + 3x) = 64 )", "Understanding the perimeter of a shape is a fundamental concept in geometry, often applied in everyday problems like fencing a garden, framing a room, or designing outdoor spaces. In this article, we’ll solve the linear perimeter equation ( 2(x + 3x) = 64 ) step by step to find the value of ( x ), showing how algebra simplifies practical geometry problems.", "---", "## What is the Perimeter in This Equation?", "The expression ( 2(x + 3x) = 64 ) represents the formula for the perimeter of a rectangular shape, where ( x ) and ( 3x ) are the lengths of two adjacent sides. Adding ( x + 3x ) gives the total length around the rectangle, and multiplying by 2 confirms the perimeter calculation:", "[
\n\ ext{Perimeter} = 2 \ imes (\ ext{length} + \ ext{width}) = 2(x + 3x) = 64
\n]", "This setup is common in real-life scenarios such as determining how much fencing is needed to enclose a rectangular plot with sides in a 1:3 ratio.", "---", "## Step-by-Step Solution", "Let’s solve the equation:", "[
\n2(x + 3x) = 64
\n]", "### Step 1: Simplify the expression inside the parentheses", "[
\nx + 3x = 4x
\n]", "Now the equation becomes:", "[
\n2(4x) = 64
\n]", "### Step 2: Multiply", "[
\n2 \ imes 4x = 8x
\n]", "So,", "[
\n8x = 64
\n]", "### Step 3: Solve for ( x )", "Divide both sides by 8:", "[
\nx = \frac{64}{8} = 8
\n]", "---", "## Interpret the Solution", "The value ( x = 8 ) represents the smaller unit measurement in the side lengths. Since one side is ( x = 8 ) units, the other side is ( 3x = 3 \ imes 8 = 24 ) units.", "Check the perimeter:", "[
\n2(8 + 24) = 2 \ imes 32 = 64
\n]", "✅ The solution confirms the perimeter equals 64 units.", "---", "## Why This Equation Matters", "This type of equation helps students connect algebra with geometric principles. By translating shapes into mathematical expressions, we can solve for unknown dimensions efficiently. The perimeter formula ( 2(x + 3x) = 64 ) is basic but critical for understanding more complex real-world problems like material estimation or construction planning.", "---", "## Real-Life Applications", "- Garden Fencing: If you’re fencing a rectangular garden where one side is 3 times the other, and the total fencing is 64 meters, find exact side lengths.
\n- Interior Design: Calculating dimensions for rooms or wall decorations based on uniform borders.
\n- Architecture Basics: Estimating perimeter for materials like flooring or framing.", "---", "## Summary", "The equation ( 2(x + 3x) = 64 ) models the perimeter of a rectangle with sides in a 1:3 ratio. Solving it yields:", "[
\nx = 8, \quad 3x = 24, \quad \ ext{Perimeter} = 64
\n]", "Mastering such algebraic manipulations strengthens problem-solving skills across STEM disciplines. Always remember: understanding the geometry behind the equation enhances practical application and reasoning.", "---", "## SEO Keywords:", "# Perimeter equation solution, solve 2(x + 3x) = 64, rectangular perimeter algebra, geometry problem solving, linear equation perimeter, rectangular shape perimeter, algebraic perimeter calculation, how to find x in perimeter, real-life geometry problems", "---", "Explore more about perimeters, equations, and algebra to build stronger math foundations—essential for students, educators, and DIY enthusiasts alike!"]
