1. **State the problem:** We need to find the length of the hypotenuse $c$ of a right triangle where the legs are 54 m and 72 m. 2. **Formula used:** According to the Pythagorean theorem, for a right triangle with legs $a$ and $b$ and hypotenuse $c$, the relationship is: $$c^2 = a^2 + b^2$$ 3. **Substitute the given values:** $$c^2 = 54^2 + 72^2$$ 4. **Calculate the squares:** $$c^2 = 2916 + 5184$$ 5. **Add the squares:** $$c^2 = 8100$$ 6. **Take the square root of both sides to solve for $c$:** $$c = \sqrt{8100}$$ 7. **Simplify the square root:** $$c = 90$$ **Final answer:** The length of the hypotenuse $c$ is 90 meters.