Final answer:
The distance between tree A and tree P in the square backyard with 30-ft sides is approximately 42.4 ft.
Step-by-step explanation:
The distance between tree A and tree P can be found using the Pythagorean theorem. Since the backyard forms a square, the distance between A and P is the same as the length of a diagonal across the square. The diagonal of a square can be found using the formula d = s√2, where d is the diagonal length and s is the side length. In this case, the side length is 30 ft, so the diagonal length is approximately 30√2 = 42.4 ft. Therefore, the distance between tree A and tree P to the nearest tenth is approximately 42.4 ft, which corresponds to option B.