Final answer:
To find the length of AC, we can use the Pythagorean theorem. By setting up two equations using the lengths of the legs and the hypotenuse, we can solve for the unknown lengths and find that the length of AC is 48*sqrt(2).
Step-by-step explanation:
To find the length of AC, we need to use the Pythagorean theorem. In triangle ABC, the length of GH (16) is the length of the vertical leg, and we need to find the length of AC, which is the hypotenuse. Using the theorem, we have AC^2 = AB^2 + BC^2. Since GH is perpendicular to AB and BC, it divides the triangle into two right triangles. Let's call the length of AB x and the length of BC y. Using the Pythagorean theorem for each right triangle, we have x^2 + 8^2 = 16^2 and y^2 + 8^2 = 16^2. Solving these equations, we find that x = 48 and y = 48. Therefore, the length of AC is sqrt(48^2 + 48^2) = sqrt(2*48^2) = 48*sqrt(2).