A 12-ft-tall fence runs parallel to a wall of a house at a distance of 24 ft. Find the length of the shortest ladder that extends from the ground to the house without touching the fence. Assume the vertical wall of the house and the horizontal ground have infinite extent. . . . Let L be the length of the ladder, x be the distance from the base of the ladder to the fence, d be the distance from the fence to the house and b be the distance from the ground to the point the ladder touches the house. What is the objective function, in terms of x? L =_ (Type an expression.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) The length of the shortest ladder is ft. (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest thousandth as needed.)