1. **Problem statement:** We need to find the length of the diagonal path of a rectangular area with length 18m and width 12m. 2. **Formula used:** The diagonal $d$ of a rectangle with length $l$ and width $w$ is given by the Pythagorean theorem: $$d = \sqrt{l^2 + w^2}$$ 3. **Substitute the values:** $$d = \sqrt{18^2 + 12^2}$$ 4. **Calculate the squares:** $$d = \sqrt{324 + 144}$$ 5. **Add the values inside the square root:** $$d = \sqrt{468}$$ 6. **Simplify the surd:** $$468 = 4 \times 117$$ $$d = \sqrt{4 \times 117} = \sqrt{4} \times \sqrt{117} = 2\sqrt{117}$$ 7. **Further simplify $\sqrt{117}$ if possible:** $$117 = 9 \times 13$$ $$d = 2 \times \sqrt{9 \times 13} = 2 \times 3 \times \sqrt{13} = 6\sqrt{13}$$ **Final answer:** The length of the diagonal path is $6\sqrt{13}$ meters.