["How to Solve the Perimeter Problem: ( 2(w + 3w) = 48 )", "When learning geometry, one of the most essential skills is solving perimeter problems efficiently. Today, we’ll walk through the equation ( 2(w + 3w) = 48 ) step-by-step to find the value of ( w ), the width of a rectangular shape. Understanding how to solve perimeter equations like this one is key for students and math enthusiasts alike.", "---", "### What is Perimeter?", "The perimeter is the total distance around the outside of a two-dimensional shape. For a rectangle, the perimeter formula is:", "[
\n\ ext{Perimeter} = 2(\ ext{length} + \ ext{width})
\n]", "In many problems, one dimension is expressed in terms of another. Here, we’re given that the perimeter equals ( 48 ) units and the length is ( 3w ), while the width is ( w ).", "---", "### Step-by-Step Solution", "We start with the perimeter equation:", "[
\n2(w + 3w) = 48
\n]", "Step 1: Simplify inside the parentheses", "Add ( w ) and ( 3w ):", "[
\nw + 3w = 4w
\n]", "Now the equation becomes:", "[
\n2(4w) = 48
\n]", "Step 2: Multiply", "Multiply ( 2 \ imes 4w = 8w ), so:", "[
\n8w = 48
\n]", "Step 3: Solve for ( w )", "Divide both sides by 8:", "[
\nw = \frac{48}{8} = 6
\n]", "---", "### Final Answer", "The value of ( w ) is ( 6 ). Since ( w ) represents the width, the rectangle’s width is 6 units. To find the length, recall ( 3w = 3 \ imes 6 = 18 ).", "So, dimensions are:", "- Width: ( 6 ) units
\n- Length: ( 18 ) units
\n- Perimeter: ( 2(6 + 18) = 48 ) — confirming our solution.", "---", "### Why This Problem Matters", "Solving equations like ( 2(w + 3w) = 48 ) builds foundational algebra skills essential for geometry, word problems, and real-world applications involving area and dimensions. Regular practice strengthens your ability to model situations mathematically and verify results logically.", "---", "In summary:
\n- Start with perimeter formula for a rectangle.
\n- Simplify expressions inside parentheses.
\n- Perform arithmetic operations carefully.
\n- Isolate the variable and solve.
\n- Check your answer by substituting back into the original equation.", "With this method, any perimeter equation can be tackled step by step. Keep practicing — you’ll master perimeter and beyond!", "---", "Keywords: perimeter equation, solve 2(w + 3w) = 48, geometry problem, algebra 2, solve for w, rectangle dimensions, math step-by-step, solve linear equations, how to find width from perimeter.
\nMeta Description: Learn how to solve the perimeter equation ( 2(w + 3w) = 48 ) step-by-step. Find ( w = 6 ) and understand the algebraic process for mastering geometry and word problems."]
