A rectangle has a length that is 3 times its width. If the perimeter is 64 meters, what are the dimensions of the rectangle?
["A Rectangle Has a Length That Is 3 Times Its Width — Find Its Dimensions When the Perimeter Is 64 Meters", "Understanding the relationship between a rectangle’s length and width is essential in geometry and real-world applications like architecture, design, and construction. Let’s explore a classic problem: If a rectangle has a length that is 3 times its width, and its perimeter is 64 meters, what are its dimensions?", "### The Formula That Matters: Perimeter of a Rectangle", "The perimeter ( P ) of a rectangle is calculated using the formula:", "[\nP = 2 \ imes (\ ext{Length} + \ ext{Width})\n]", "In this problem, we know:", "- The length (( L )) is 3 times the width (( W )), so ( L = 3W )\n- The total perimeter is 64 meters", "### Step-by-Step Calculation", "1. Substitute the length into the perimeter formula:", "[\n64 = 2 \ imes (3W + W)\n]", "2. Simplify inside the parentheses:", "[\n64 = 2 \ imes 4W\n]", "[\n64 = 8W\n]", "3. Solve for ( W ):", "[\nW = \frac{64}{8} = 8 \ ext{ meters}\n]", "4. Find the length using ( L = 3W ):", "[\nL = 3 \ imes 8 = 24 \ ext{ meters}\n]", "### Conclusion: Dimensions of the Rectangle", "With a perimeter of 64 meters and the length 3 times the width, the rectangle’s dimensions are:", "- Width: 8 meters\n- Length: 24 meters", "This solution highlights how algebraic relationships help solve real-life geometry problems efficiently. Whether calculating space for a garden, planning a room layout, or designing props, knowing how to use proportions and formulas is invaluable.", "Keywords: rectangle perimeter formula, length is 3 times width, solve rectangle dimensions, geometry problem solution, 64-meter perimeter rectangle, rectangle width and length calculation.", "---\nNeed help with geometry or spatial planning? Understanding rectangle dimensions unlocks clearer approaches to any design challenge!"]
