A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 64 meters, what is the width of the rectangle?
["How to Find the Width of a Rectangle When Length Is 3 Times the Width and the Perimeter Is 64 Meters", "Understanding basic geometry can help solve everyday problems efficiently—especially when working with rectangles. One common question in math and design is determining the dimensions of a rectangle given the relationship between its length and width and its perimeter. In this article, we’ll walk through how to calculate the width of a rectangle where the length is three times the width, and the perimeter measures 64 meters.", "### The Relationship Between Length and Width", "We start with the information that the length (L) is 3 times the width (W). This relationship can be written mathematically as:\n[ L = 3W ]", "This simple equation is key—it connects the two unknowns, allowing us to express everything in terms of one variable, the width.", "### Formula for the Perimeter of a Rectangle", "The perimeter ( P ) of a rectangle is calculated using the formula:\n[ P = 2L + 2W ]\nPlugging in the known perimeter:\n[ 64 = 2L + 2W ]", "### Substitute the Length in Terms of Width", "Since ( L = 3W ), substitute this into the perimeter equation:\n[ 64 = 2(3W) + 2W ]\nSimplify:\n[ 64 = 6W + 2W ]\n[ 64 = 8W ]", "### Solve for the Width", "Now, isolate ( W ) by dividing both sides by 8:\n[ W = \frac{64}{8} ]\n[ W = 8 ]", "### Final Answer", "The width of the rectangle is 8 meters.\nUsing this, the length is ( 3 \ imes 8 = 24 ) meters, and indeed, the perimeter is:\n[ 2(24) + 2(8) = 48 + 16 = 64 \ ext{ meters} ],\nconfirming our solution.", "### Why This Matters", "Whether you're designing a room, fabric, or packaging, accurately calculating dimensions based on shape relationships saves time and ensures precision. Knowing how to apply formulas like perimeter and proportional relationships helps streamline problem-solving in both classroom and real-world settings.", "---", "Summary:\n- Rectangle length = 3 × width\n- Perimeter = 64 meters\n- Width = 8 meters\n- Use ( L = 3W ) and perimeter formula to find dimensions efficiently", "Keywords: rectangle perimeter, width calculation, length 3 times width, geometry problem, math tutorial"]
