1. **State the problem:** We need to find the length of the diagonal path across a square garden that measures 100 feet on each side. 2. **Formula used:** The diagonal $d$ of a square with side length $s$ is given by the Pythagorean theorem: $$d = \sqrt{s^2 + s^2} = \sqrt{2s^2} = s\sqrt{2}$$ 3. **Apply the formula:** Here, $s = 100$ feet. $$d = 100 \times \sqrt{2}$$ 4. **Calculate the value:** $$d = 100 \times 1.4142 = 141.42$$ 5. **Round to the nearest foot:** $$d \approx 141$$ feet **Final answer:** The path along the diagonal will be approximately 141 feet long.