Question:** A rectangle has a perimeter of 48 cm and a length that is twice its width. What are the dimensions of the rectangle?
["Finding the Dimensions of a Rectangle: Perimeter, Length, and Width Explained", "If you’ve ever wondered how to calculate the dimensions of a rectangle when given its perimeter and a relationship between its length and width, you’re in the right place. Let’s dive into a clear, step-by-step explanation of a classic geometry problem:", "Question: A rectangle has a perimeter of 48 cm and a length that is twice its width. What are the dimensions of the rectangle?", "---", "### Understanding the Problem", "A rectangle’s perimeter is the total distance around its outer edges. The formula for the perimeter ( P ) of a rectangle is:\n[\nP = 2 \ imes (\ ext{length} + \ ext{width})\n]\nWe’re given:\n- ( P = 48 ) cm\n- ( \ ext{length} = 2 \ imes \ ext{width} )", "Let’s define the variables:\nLet the width = ( x ) cm\nThen the length = ( 2x ) cm", "---", "### Applying the Perimeter Formula", "Substitute the known values into the perimeter formula:\n[\n48 = 2 \ imes (2x + x)\n]", "Simplify inside the parentheses:\n[\n48 = 2 \ imes (3x)\n]", "Multiply:\n[\n48 = 6x\n]", "---", "### Solving for the Width", "Divide both sides by 6:\n[\nx = \frac{48}{6} = 8\n]", "So, the width is 8 cm.", "---", "### Finding the Length", "Since the length is twice the width:\n[\n\ ext{Length} = 2x = 2 \ imes 8 = 16 \ ext{ cm}\n]", "---", "### Final Answer: Dimensions of the Rectangle", "- Width = 8 cm\n- Length = 16 cm", "---", "### Why This Method Works", "Breaking down the problem into variables and applying a well-known formula allows for a straightforward algebraic solution. Understanding the relationship between perimeter, length, and width helps solve similar real-world problems—such as calculating materials for construction, designing layouts, or teaching math students.", "---", "### Key Takeaways\n- Use ( P = 2(l + w) ) for perimeter calculations.\n- Substitute known relationships like “length = 2 × width” into the formula.\n- Solve algebraically to find exact dimensions.", "If you’re learning geometry or solving word problems, practice this structured approach—it makes figuring out unknowns faster and more confident!", "---\nKeywords: Rectangle dimensions, perimeter formula, length and width relationship, algebra geometry, solve rectangle problem, step-by-step geometry, fix rectangle dimensions, math problem solution, rectangle problems, 48 cm perimeter, width calculation, length calculation."]
