Answer:
diagonal length = 12√2 inches
Step-by-step explanation:
If the perimeter of the square is 48 inches, the length of one side is one fourth of that, or 12 inches. The diagonal creates a 45-45-90 triangle with two 12-in legs; we are to find the length of the diagonal. Using the Pythagorean Theorem, we get
12² + 12² = (diagonal length)², or 2(12²) = (diagonal length)²
Taking the square root of both sides, we get:
diagonal length = 12√2 inches
