1. **State the problem:** We need to find the perimeter of a right-angled triangle with legs measuring 3 m and 14 m. 2. **Formula used:** The perimeter $P$ of a triangle is the sum of all its sides. For a right-angled triangle with legs $a$ and $b$, and hypotenuse $c$, the perimeter is: $$P = a + b + c$$ 3. **Find the hypotenuse using Pythagoras' theorem:** $$c = \sqrt{a^2 + b^2}$$ Substitute $a=3$ and $b=14$: $$c = \sqrt{3^2 + 14^2} = \sqrt{9 + 196} = \sqrt{205}$$ 4. **Calculate the numerical value of $c$:** $$c \approx 14.3178$$ 5. **Calculate the perimeter:** $$P = 3 + 14 + 14.3178 = 31.3178$$ 6. **Round to 1 decimal place:** $$P \approx 31.3$$ **Final answer:** The perimeter of the triangle is approximately $31.3$ meters.