A rectangle has a length that is 3 times its width. If the perimeter is 96 meters, what is the width?
["# Finding the Width of a Rectangle: A 3:1 Length-to-Width Ratio with a Perimeter of 96 Meters", "Understanding the dimensions of rectangles is essential in geometry and practical applications, from architecture to interior design. Today, we’ll solve a classic geometry problem: determining the width of a rectangle when its length is three times its width and its perimeter is 96 meters. This scenario perfectly illustrates how mathematical relationships and formulas like the perimeter help unlock real-world measurements.", "## The Problem: Given Ratios and Perimeter", "We are told:", "- The length ( L ) is 3 times the width ( W ) → ( L = 3W )\n- The perimeter ( P = 96 ) meters", "We aim to find the value of the width ( W ).", "## Step 1: Recall the Perimeter Formula for a Rectangle", "The perimeter ( P ) of a rectangle is calculated using:", "[\nP = 2 \ imes (L + W)\n]", "Substituting the known perimeter:", "[\n96 = 2 \ imes (L + W)\n]", "## Step 2: Substitute Length in Terms of Width", "Since ( L = 3W ), replace ( L ) in the perimeter equation:", "[\n96 = 2 \ imes (3W + W)\n]", "[\n96 = 2 \ imes 4W\n]", "[\n96 = 8W\n]", "## Step 3: Solve for Width", "Divide both sides by 8:", "[\nW = \frac{96}{8} = 12\n]", "## Conclusion: The Width is 12 Meters", "The width of the rectangle is 12 meters. Using this relationship:", "- Width = 12 m\n- Length = ( 3 \ imes 12 = 36 ) m\n- Perimeter = ( 2 \ imes (12 + 36) = 2 \ imes 48 = 96 ) m — matches perfectly.", "### Bonus Insight", "This problem demonstrates how a simple proportional relationship — length 3 times width — combined with the perimeter formula allows precise calculation of unknown dimensions. Whether you're designing a room, calculating fence requirements, or solving geometry homework, understanding these principles makes solving real-world problems efficient and accurate.", "---", "Keywords: rectangle perimeter, length = 3 × width, 3:1 rectangle ratio, find width given perimeter, geometry problem solution, math tutorial", "Meta Description: Learn how to calculate the width of a rectangle with a 3:1 length-to-width ratio and a perimeter of 96 meters using algebra and geometry fundamentals."]
