A rectangle has a length that is three times its width. If the perimeter of the rectangle is 96 cm, what is the area of the rectangle?
["Finding the Area of a Rectangle: When Length Is Three Times Its Width", "Understanding the relationship between a rectangle’s dimensions is essential in geometry—and one common problem involves a rectangle where the length is three times the width. This type of calculation not only reinforces algebraic thinking but also helps in real-world applications like design, construction, and area estimation.", "In this article, we’ll explore how to find the area of a rectangle when you know that the length (L) is three times its width (W), and the perimeter is 96 cm. Let’s break it down step-by-step.", "---", "### Understanding the Rectangle Dimensions", "Given:\n- Length = 3 × Width → L = 3W\n- Perimeter (P) = 96 cm", "The formula for the perimeter of a rectangle is:\n[\nP = 2(L + W)\n]", "Substituting the known values:\n[\n96 = 2(3W + W)\n]", "Simplify inside the parentheses:\n[\n96 = 2(4W) = 8W\n]", "Solve for width (W):\n[\nW = \frac{96}{8} = 12 \ ext{ cm}\n]", "Now find the length:\n[\nL = 3W = 3 \ imes 12 = 36 \ ext{ cm}\n]", "---", "### Calculating the Area", "The area (A) of a rectangle is given by:\n[\nA = L \ imes W\n]", "Substitute the known values:\n[\nA = 36 \ imes 12 = 432 \ ext{ cm}^2\n]", "---", "### Conclusion", "When a rectangle’s length is three times its width and its perimeter is 96 cm, the area is 432 square centimeters. This algebraic method efficiently solves many real-world problems involving rectangular spaces—making it a valuable skill in math, architecture, and design.", "Mastering these computing steps not only improves numerical reasoning but also empowers you to tackle similar geometry problems with confidence.", "---", "Key Search Terms:\nrectangle area formula, rectangle length three times width, rectangle perimeter 96 cm, how to calculate rectangle area, algebraic rectangle problem, geometry problems with ratios, real-world rectangle measurements", "Meta Title: How to Calculate the Area of a Rectangle When Length is Three Times the Width\nMeta Description: Learn step-by-step how to find the area of a rectangle with a length three times its width using perimeter data (96 cm), including correct formulas and real-world applications."]
