1. **State the problem:** We need to find the perimeter of a right-angled triangle with sides 8 cm (vertical), 3 cm (horizontal adjacent to the right angle), and a base segment of 15 cm extending beyond the right angle. 2. **Identify the sides:** The triangle has one vertical side of 8 cm, a horizontal side adjacent to the right angle of 3 cm, and the hypotenuse is the side opposite the right angle. The base is split into 3 cm and 15 cm segments, so the total base length is $3 + 15 = 18$ cm. 3. **Use the Pythagorean theorem:** Since the right angle is between the 8 cm and 3 cm sides, the hypotenuse $c$ is calculated as: $$c = \sqrt{8^2 + 3^2} = \sqrt{64 + 9} = \sqrt{73}$$ 4. **Calculate the hypotenuse:** $$c = \sqrt{73} \approx 8.544\text{ cm}$$ 5. **Calculate the perimeter:** The perimeter $P$ is the sum of all three sides: $$P = 8 + 3 + 8.544 = 19.544\text{ cm}$$ 6. **Round to 1 decimal place:** $$P \approx 19.5\text{ cm}$$ **Final answer:** The perimeter of the triangle is approximately **19.5 cm**.