A rectangle has a length of 12 meters and a width of 8 meters. What is the area of the rectangle, and what is the length of its diagonal, rounded to the nearest tenth?
["How to Calculate the Area and Diagonal of a Rectangle: A Step-by-Step Guide", "Understanding basic geometry is essential for a variety of real-world applications—whether you're designing a room, planning a garden, or solving everyday measurement problems. One of the most common shapes encountered is the rectangle, defined by its length and width. In this article, we’ll explore a simple yet practical example: a rectangle with a length of 12 meters and a width of 8 meters. We’ll calculate its area and diagonal length, offering clear steps and useful mathematical insights.", "### What Are the Dimensions of the Rectangle?", "According to the given measurements:\n- Length = 12 meters\n- Width = 8 meters", "These dimensions allow us to perform key geometric computations.", "---", "### Step 1: Calculate the Area of the Rectangle", "The area of a rectangle is found using the formula:\n[\n\ ext{Area} = \ ext{Length} \ imes \ ext{Width}\n]\nSubstituting the values:\n[\n\ ext{Area} = 12, \ ext{m} \ imes 8, \ ext{m} = 96, \ ext{m}^2\n]\nSo, the area of the rectangle is 96 square meters—a fundamental measurement useful for planning space usage.", "---", "### Step 2: Calculate the Diagonal Length", "To find the rectangle’s diagonal—the straight line connecting two opposite corners—we apply the Pythagorean Theorem. Since the rectangle’s diagonal splits it into two right-angled triangles, the formula is:\n[\n\ ext{Diagonal} = \sqrt{\ ext{Length}^2 + \ ext{Width}^2}\n]\nPlugging in the values:\n[\n\ ext{Diagonal} = \sqrt{12^2 + 8^2} = \sqrt{144 + 64} = \sqrt{208}\n]\nNow, compute the square root:\n[\n\sqrt{208} \approx 14.4 \quad \ ext{(rounded to the nearest tenth)}\n]\nThus, the diagonal measures approximately 14.4 meters, providing vital information for applications like framing or installation.", "---", "### Summary of Results", "- Area: 96 m²\n- Diagonal: ≈ 14.4 meters (rounded to the nearest tenth)", "This calculation demonstrates how simple geometry enables precise measurements in construction, engineering, and design. Whether you're calculating floor space or cutting materials, knowing how to compute area and diagonal length of a rectangle is an indispensable skill.", "Stay tuned for more practical math tips that bring clarity to everyday problem-solving!"]
