A rectangle's length is 3 times its width. If the perimeter of the rectangle is 48 meters, what is the area of the rectangle?
["Title: How to Calculate the Area of a Rectangle When Length is 3 Times Its Width – A Step-by-Step Guide", "When solving geometry problems, understanding relationships between a rectangle’s length, width, perimeter, and area is essential. One common scenario involves a rectangle where the length is 3 times the width, and the perimeter is given—in this case, 48 meters. In this article, we’ll walk through the process of finding the rectangle’s area using basic algebra and geometry formulas.", "---", "### Understanding the Problem", "You’re told:\n- The length (L) is 3 times the width (W)\n- The perimeter is 48 meters", "We are asked to find the area of the rectangle after calculating its dimensions.", "---", "### Step 1: Set Up the Relationship Between Length and Width", "Given:\n[\nL = 3W\n]", "---", "### Step 2: Use the Perimeter Formula", "The perimeter (P) of a rectangle is given by:\n[\nP = 2L + 2W\n]", "Substitute the given perimeter and the expression for L:\n[\n48 = 2(3W) + 2W\n]", "---", "### Step 3: Simplify the Equation", "[\n48 = 6W + 2W\n]\n[\n48 = 8W\n]", "Now, solve for W:\n[\nW = \frac{48}{8} = 6 \ ext{ meters}\n]", "---", "### Step 4: Find the Length", "Using ( L = 3W ):\n[\nL = 3 \ imes 6 = 18 \ ext{ meters}\n]", "---", "### Step 5: Calculate the Area", "Area (A) of a rectangle is:\n[\nA = L \ imes W\n]", "Substitute values:\n[\nA = 18 \ imes 6 = 108 \ ext{ square meters}\n]", "---", "### Final Answer: Area = 108 m²", "---", "### Summary", "- Width (W) = 6 meters\n- Length (L) = 18 meters\n- Perimeter = 48 meters (confirmed)\n- Area = 108 m²", "By relating the rectangle’s dimensions algebraically and solving step-by-step using perimeter data, we efficiently determine both dimensions and area. This method is valuable for solving similar geometry problems efficiently and accurately—key for students, educators, and anyone interested in math applications.", "---", "Keywords: rectangle area, rectangle dimensions, perimeter formula, 3 times width rectangle, algebra geometry problem, how to find rectangle area, length is 3 times width, math problem solution", "---", "Don’t miss out on mastering these core geometry principles—practice with similar problems to build confidence and speed!"]
