A rectangle has a length that is twice its width. If the perimeter of the rectangle is 60 meters, what is the area of the rectangle?
["How to Calculate the Area of a Rectangle with a Given Perimeter: A Practical Example", "Understanding the relationship between a rectangle’s dimensions and its perimeter is essential in geometry and everyday applications like construction, gardening, and interior design. In this article, we’ll explore a classic problem: determining the area of a rectangle when the length is twice the width and the perimeter is known.", "### Given:\n- A rectangle has a length ( L ) that is twice its width ( W ), so:\n [\n L = 2W\n ]\n- The perimeter ( P ) of the rectangle is 60 meters.", "### Step 1: Recall the Perimeter Formula\nThe perimeter ( P ) of a rectangle is calculated using:\n[\nP = 2L + 2W\n]\nSubstitute the given perimeter:\n[\n60 = 2L + 2W\n]", "### Step 2: Substitute Length with Width\nSince ( L = 2W ), replace ( L ) in the perimeter equation:\n[\n60 = 2(2W) + 2W\n]\n[\n60 = 4W + 2W\n]\n[\n60 = 6W\n]\nSolve for ( W ):\n[\nW = \frac{60}{6} = 10 \ ext{ meters}\n]", "### Step 3: Calculate the Length\nNow find ( L ):\n[\nL = 2W = 2 \ imes 10 = 20 \ ext{ meters}\n]", "### Step 4: Calculate the Area\nThe area ( A ) of a rectangle is given by:\n[\nA = L \ imes W\n]\nSubstitute the known values:\n[\nA = 20 \ imes 10 = 200 \ ext{ square meters}\n]", "### Conclusion\nWhen a rectangle’s length is twice its width and its perimeter is 60 meters, its area is 200 square meters. This straightforward approach using algebraic substitution ensures accuracy in solving real-world geometric problems.", "Whether you're designing a room, laying a garden bed, or planning a construction project, knowing how to calculate area from given perimeter and dimension ratios is invaluable.", "Keywords: rectangle area, perimeter calculation, geometry problem, rectangle dimensions, length twice width, 60 meter perimeter, area formula, algebra in geometry", "Meta Description: Solve a geometry problem: a rectangle with length twice its width and a 60-meter perimeter. Learn how to find the area step-by-step."]
