Question**: A rectangle has a perimeter of 48 cm and a length that is twice its width. Find its area.
["Title: How to Find the Area of a Rectangle: Solve Using Perimeter and Length-Width Relationship", "Meta Description: Learn how to find the area of a rectangle step-by-step using perimeter and the relationship between length and width. Solve a real problem: a rectangle with a 48 cm perimeter and length twice its width.", "---", "### Introduction\nMathematics often presents puzzles that combine relationships between shapes and numerical values. One common problem involves rectangles, where understanding how perimeter relates to dimensions helps uncover hidden properties—like area. In this article, we’ll explore how to find the area of a rectangle with a perimeter of 48 cm and a length that is twice its width.", "### Understanding the Problem\nYou’re given:\n- Perimeter = 48 cm\n- Length ( L ) is twice the width ( W ), so ( L = 2W )", "Your goal is to find the area, calculated as ( A = L \ imes W ).", "Why solving for dimensions first?\nSince only perimeter and the ratio between length and width are provided, algebraic geometry allows us to express everything in terms of one variable, simplify, and solve.", "### Step-by-Step Solution", "1. Write the perimeter formula:\nThe perimeter ( P ) of a rectangle is\n[\nP = 2L + 2W\n]\nSubstitute ( P = 48 ) cm and ( L = 2W ):\n[\n48 = 2(2W) + 2W\n]", "2. Simplify the equation:\n[\n48 = 4W + 2W\n]\n[\n48 = 6W\n]", "3. Solve for width ( W ):\n[\nW = \frac{48}{6} = 8 \ ext{ cm}\n]", "4. Find the length ( L ):\nSince ( L = 2W ):\n[\nL = 2 \ imes 8 = 16 \ ext{ cm}\n]", "5. Calculate the area:\n[\nA = L \ imes W = 16 \ imes 8 = 128 \ ext{ cm}^2\n]", "### Final Answer\nThe area of the rectangle is 128 square centimeters.", "### Why This Method Works\nBy expressing both length and width in terms of width using the given ratio, we reduce the problem to a simple linear equation. Solving it step-by-step reveals not just area but also individual dimensions—essential for real-world applications like design, construction, or education.", "### Bonus Tip: Always Check Your Work\nAfter solving, plug values back into the original equations:\n- Perimeter: ( 2(16) + 2(8) = 32 + 16 = 48 ) ✔\n- Length is twice width: ( 16 = 2 \ imes 8 ) ✔", "This ensures your solution is correct and meaningful.", "---", "Keywords: rectangle area formula, perimeter and length width rectangle, solve rectangle dimensions, how to find rectangle area, step-by-step geometry problem", "For more geometry insights, subscribe and explore endless problems at [YourWebsiteName]!"]
