A rectangle has a perimeter of 48 cm. If the length is 3 times the width, find the dimensions of the rectangle.
["Title: How to Find the Dimensions of a Rectangle with a Perimeter of 48 cm and Length 3 Times the Width", "---", "Introduction", "Understanding the relationship between a rectangle’s perimeter, length, and width is a fundamental concept in geometry — especially valuable for students, educators, and anyone interested in real-world problem solving. In this article, we’ll explore how to determine the exact dimensions of a rectangle when given its perimeter (48 cm) and the condition that the length is 3 times the width. Whether you’re preparing for a math exam or solving a practical measurement problem, this guide will help you find the solution step by step.", "---", "### Understanding the Problem", "We are told:\n- The rectangle’s perimeter is 48 cm.\n- The length (L) is 3 times the width (W).", "We want to find both the length and width of the rectangle.", "---", "### What You Need to Know", "Perimeter of a rectangle is calculated using the formula:\n[\nP = 2L + 2W\n]\nwhere\n- ( P ) = perimeter\n- ( L ) = length\n- ( W ) = width", "Given:\n[\nP = 48 , \ ext{cm}, \quad L = 3W\n]", "---", "### Step-by-Step Solution", "Step 1: Substitute the length in terms of width into the perimeter formula.\n[\n48 = 2(3W) + 2W\n]", "Step 2: Simplify the equation.\n[\n48 = 6W + 2W\n]\n[\n48 = 8W\n]", "Step 3: Solve for width.\n[\nW = \frac{48}{8} = 6 , \ ext{cm}\n]", "Step 4: Calculate the length using ( L = 3W ).\n[\nL = 3 \ imes 6 = 18 , \ ext{cm}\n]", "---", "### Final Answer", "The dimensions of the rectangle are:\n- Width = 6 cm\n- Length = 18 cm", "---", "### Why This Matters", "Knowing how to derive unknown side lengths from perimeter and proportional relationships helps in architecture, interior design, farming (calculating fence needs), and everyday measurements. This problem demonstrates the power of algebra with geometry — turning word problems into precise calculations.", "---", "### Summary", "- Given: Perimeter = 48 cm; length = 3 × width\n- Use perimeter formula: ( P = 2L + 2W )\n- Substitute ( L = 3W ) → ( 48 = 2(3W) + 2W )\n- Solve: ( W = 6 , \ ext{cm}, L = 18 , \ ext{cm} )", "---", "### FAQ: Common Questions About Rectangle Perimeters", "Q: How do I find width when length is known and proportional?\nA: Express length in terms of width, substitute into perimeter formula, and solve algebraically.", "Q: Can I use this method for other shapes or perimeters?\nA: Yes! This algebraic approach is widely applicable for rectangles, parallelograms, and any shape where perimeter depends on side lengths.", "---", "### Key Takeaways", "- Knowing ( P = 2(L + W) ) is key to solving perimeter problems.\n- Expressing sides in terms of a single variable simplifies solving.\n- Always substitute known expressions into the formula to find the unknown.", "---", "References:\n- Basic geometry textbooks\n- Online algebra solvers and geometry resources\n- School-level mathematics curricula", "---", "Ready to calculate next? Try solving more puzzles involving rectangles — your next math challenge awaits!"]
