1. **Problem Statement:** Given a right-angled triangle with one leg (height) 2.7 m and the other leg (base) 70 cm (0.7 m), and a step pattern along the hypotenuse with steps of 6 cm height and 8 cm base. We need to find: (i) The total height of the stepped path. (ii) The length of one step along the hypotenuse. (iii) Whether the stepped path is longer than the hypotenuse. (iv) The length of the hypotenuse AB. (v) The total length of the stepped path. 2. **Formulas and Important Rules:** - Pythagoras theorem for right triangle: $$c = \sqrt{a^2 + b^2}$$ where $c$ is hypotenuse. - Length of each step along hypotenuse can be found using Pythagoras on step dimensions. - Total number of steps = total vertical height / step height. 3. **Calculations:** (i) Total height of stepped path = height of triangle = 2.7 m = 270 cm. Number of steps = $$\frac{270}{6} = 45$$ steps. (ii) Length of one step along hypotenuse: Step base = 8 cm, step height = 6 cm. Length of one step = $$\sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10\text{ cm}$$. (iii) Length of hypotenuse AB: Base = 70 cm, height = 270 cm. $$AB = \sqrt{70^2 + 270^2} = \sqrt{4900 + 72900} = \sqrt{77800} \approx 278.9\text{ cm}$$. (iv) Total length of stepped path = number of steps $\times$ length of one step = $$45 \times 10 = 450\text{ cm}$$. (v) Compare stepped path length and hypotenuse: Stepped path length = 450 cm, hypotenuse = 278.9 cm. Since 450 cm > 278.9 cm, the stepped path is longer than the hypotenuse. **Final answers:** (i) Total stepped height = 2.7 m. (ii) Length of one step = 10 cm. (iii) Stepped path is longer than hypotenuse. (iv) Hypotenuse AB length $\approx$ 2.789 m. (v) Total stepped path length = 4.5 m.