1. **State the problem:** We need to find the shortest length of a hose extending from the southwest corner to the northeast corner of a rectangular swimming pool with length 48 feet and width 36 feet. 2. **Formula used:** The shortest distance between two opposite corners of a rectangle is the length of the diagonal, which can be found using the Pythagorean theorem: $$d = \sqrt{l^2 + w^2}$$ where $l$ is the length and $w$ is the width. 3. **Calculate the diagonal:** $$d = \sqrt{48^2 + 36^2} = \sqrt{2304 + 1296} = \sqrt{3600}$$ 4. **Simplify the square root:** $$d = \sqrt{3600} = 60$$ 5. **Conclusion:** The shortest length the hose can be is 60 feet. **Answer: 60 feet**