If the perimeter of a square is 8 cm , what is the length of the diagonal? (1 point) ( \( \frac{\sqrt{2}}{2} \mathrm{~cm} \) \( 2 \sqrt{2} \mathrm{~cm} \) 4 cm \( 4 \sqrt{2} \mathrm{~cm} \) Check answer Remaining Attempts : 3

To find the length of the diagonal of a square, you first need to determine the side length. Given the perimeter is 8 cm, you can divide that by 4 (since a square has 4 equal sides) to find that each side is 2 cm long. Now, use the diagonal formula \(d = s\sqrt{2}\). Plugging in our side length, \(d = 2\sqrt{2}\) cm. So, the correct answer is \(2\sqrt{2} \mathrm{~cm}\). Did you know that the relationship between the side length and the diagonal is a classic problem from geometry? It stems from the Pythagorean theorem, where the diagonal essentially serves as the hypotenuse of a right triangle formed by two sides of the square. This fundamental concept has been around for centuries, showing just how interconnected mathematics is with our understanding of shapes and spaces! For practical applications, understanding the diagonal of a square is vital in fields like architecture and design. When creating blueprints, architects rely on these calculations to ensure that spaces are proportionate and structurally sound. Knowing how to swiftly calculate dimensions can save time and resources, making it an essential skill in various trades!