A rectangle's length is twice its width. If the perimeter is 36 cm, what is the area of the rectangle?

A rectangle's length is twice its width. If the perimeter is 36 cm, what is the area of the rectangle?

["# How to Calculate the Area of a Rectangle with a Given Length-to-Width Ratio and Perimeter", "Understanding the relationship between a rectangle’s length, width, perimeter, and area is essential in geometry. Whether you’re designing a room, planning a garden layout, or solving math problems, knowing how to work with these properties can simplify your calculations. In this article, we’ll explore how to find the area of a rectangle when its length is twice its width and its perimeter measures 36 cm.", "## The Relationship Between Length and Width", "If the rectangle’s length ((L)) is twice its width ((W)), we can express this relationship mathematically:", "[\nL = 2W\n]", "Knowing this key fact helps us set up the equation for the perimeter, a fundamental property of rectangles.", "## Using the Perimeter to Find Dimensions", "The formula for the perimeter (P) of a rectangle is:", "[\nP = 2L + 2W\n]", "Given that (P = 36) cm, we substitute (L = 2W) into the perimeter formula:", "[\n36 = 2(2W) + 2W\n]", "Simplify the expression:", "[\n36 = 4W + 2W\n]\n[\n36 = 6W\n]", "Solve for (W):", "[\nW = \frac{36}{6} = 6 \ ext{ cm}\n]", "Now use (L = 2W) to find the length:", "[\nL = 2 \ imes 6 = 12 \ ext{ cm}\n]", "## Calculating the Area", "With both length and width known, the area ((A)) of the rectangle is:", "[\nA = L \ imes W = 12 \ imes 6 = 72 \ ext{ cm}^2\n]", "## Summary", "Given a rectangle where the length is twice the width and the perimeter is 36 cm:", "- Width = 6 cm\n- Length = 12 cm\n- Area = 72 cm²", "This simple ratio and perimeter method makes finding key measurements straightforward. Understanding how length and width relate allows you to solve similar problems efficiently—ideal for students, DIY enthusiasts, and anyone working with geometric shapes.", "By mastering this approach, you’ll confidently calculate not only areas but also expand your skills in geometry!"]

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Best: assume typo and use $2.50 but accept non-integer? No.Alternatively, solve as is and report exact.But in math olympiad, problems have integer solutions.Lets assume the cost is $2.00 instead? But not.But per instruction, generate valid question.Or change total items to 120, revenue $243.75?Accept that in real context, restaurant may round, but for math, perhaps the problem is designed with integers.Alternatively, use different numbers.But to proceed, assume the calculation is accepted as is:Despite non-integer, ratio holds, but for discrete items, no solution.