1. **Problem statement:** Calculate the perimeter of a right-angled triangle with legs of lengths 7 m and 16 m. 2. **Formula:** The perimeter $P$ of a triangle is the sum of the lengths of all its sides. 3. Since this is a right-angled triangle, use the Pythagorean theorem to find the hypotenuse $c$: $$c = \sqrt{7^2 + 16^2}$$ 4. Calculate the squares: $$c = \sqrt{49 + 256}$$ 5. Sum inside the square root: $$c = \sqrt{305}$$ 6. Find the square root: $$c \approx 17.464\text{ m}$$ 7. Now, calculate the perimeter: $$P = 7 + 16 + 17.464$$ 8. Sum the sides: $$P = 40.464\text{ m}$$ 9. Round to 1 decimal place: $$P \approx 40.5\text{ m}$$ **Final answer:** The perimeter of the triangle is approximately $40.5$ meters.