A rectangle has a length that is twice its width. If the perimeter is 72 meters, find the area of the rectangle.
["# Find the Area of a Rectangle When Length is Twice Its Width and Perimeter Is 72 Meters", "Understanding the relationship between a rectangle’s length, width, and perimeter is essential for solving geometry problems efficiently. In this article, we’ll explore how to calculate the area of a rectangle when the length is twice the width and the total perimeter is 72 meters.", "## The Problem Statement", "A rectangle has a length that is twice its width. The perimeter of the rectangle is 72 meters. Our goal is to determine the area of this rectangle.", "---", "## Step-by-Step Solution", "### Step 1: Define Variables", "Let the width of the rectangle be ( w ) meters.\nSince the length is twice the width, the length is ( 2w ) meters.", "### Step 2: Use the Perimeter Formula", "The perimeter ( P ) of a rectangle is given by:\n[\nP = 2 \ imes (\ ext{length} + \ ext{width})\n]\nSubstituting the known values:\n[\n72 = 2 \ imes (2w + w)\n]", "### Step 3: Solve for ( w )", "Simplify inside the parentheses:\n[\n72 = 2 \ imes 3w\n]\n[\n72 = 6w\n]\nNow, divide both sides by 6:\n[\nw = \frac{72}{6} = 12 \ ext{ meters}\n]", "### Step 4: Find the Length", "Since length ( l = 2w ):\n[\nl = 2 \ imes 12 = 24 \ ext{ meters}\n]", "### Step 5: Calculate the Area", "The area ( A ) of a rectangle is:\n[\nA = \ ext{length} \ imes \ ext{width} = l \ imes w\n]\nSubstitute the values:\n[\nA = 24 \ imes 12 = 288 \ ext{ square meters}\n]", "---", "## Conclusion", "With a perimeter of 72 meters and a length that is twice the width, the rectangle measures 24 meters long and 12 meters wide, yielding an area of 288 square meters.", "This simple algebraic approach helps visualize how geometric properties interact. Whether solving problems for school, construction, or design, understanding these relationships makes finding areas and perimeters straightforward.", "---", "## Key Takeaways", "- Let width = ( w ); then length = ( 2w )\n- Use perimeter formula: ( P = 2(l + w) )\n- Solving ( 72 = 2(2w + w) ) gives ( w = 12 )\n- Area = ( 24 \ imes 12 = 288 , \ ext{m}^2 )", "---\nKeywords: rectangle area, perimeter formula, length twice width, solve rectangle problem, geometry exercise, math solution, width and length rectangle, 72-meter rectangle area.\nMeta Description: Find how to calculate the area of a rectangle when the length is twice the width and the perimeter is 72 meters. Step-by-step solution with final area: 288 m²."]
