A rectangle's length is three times its width. If the perimeter of the rectangle is 48 meters, what is the area of the rectangle?
["Rectangle Perimeter and Area: How to Calculate Area When Length Is Three Times Width | Step-by-Step Guide", "Understanding the relationship between a rectangle’s length and width can simplify complex geometry problems—especially when the perimeter is known. In this article, we’ll walk through how to determine the area of a rectangle where the length is three times the width, given a perimeter of 48 meters. Whether you're a student, teacher, or DIY enthusiast, this step-by-step guide will help you master rectangle calculations.", "### Given:\n- Length (L) = 3 × Width (W)\n- Perimeter = 48 meters", "### Step 1: Recall the Rectangle Perimeter Formula\nThe perimeter (P) of a rectangle is calculated using the formula:\n[ P = 2 \ imes (L + W) ]", "Substitute the known values:\n[ 48 = 2 \ imes (3W + W) ]", "### Step 2: Simplify the Equation\nCombine like terms inside the parentheses:\n[ 48 = 2 \ imes (4W) ]\n[ 48 = 8W ]", "### Step 3: Solve for Width (W)\nDivide both sides by 8:\n[ W = \frac{48}{8} = 6 \ ext{ meters} ]", "### Step 4: Calculate Length (L)\nSince ( L = 3W ):\n[ L = 3 \ imes 6 = 18 \ ext{ meters} ]", "### Step 5: Calculate the Area\nThe area (A) of a rectangle is given by:\n[ A = L \ imes W ]\nSubstitute the known values:\n[ A = 18 \ imes 6 = 108 \ ext{ square meters} ]", "---", "Conclusion:\nWhen a rectangle’s length is three times its width and the perimeter is 48 meters, the area is exactly 108 square meters. This method applies to any rectangle where one dimension is a multiple of the other—and knowing the perimeter allows easy calculation of all key measurements and area.", "If you're solving similar problems, remember to substitute variables carefully, simplify equations, and always double-check units. Understanding these fundamentals makes geometry easier and more intuitive!", "---", "Keywords: rectangle area, rectangle perimeter, geometry problems, length and width relationship, how to calculate area from perimeter, step-by-step rectangle calculation, algebra rectangle, geometry formula, width and length rectangle, perimeter to area conversion, 108 square meter rectangle", "Meta Description:\nLearn how to find the area of a rectangle when its length is three times the width and the perimeter is 48 meters. Step-by-step solution with formula application and final area = 108 m²."]
