1. **State the problem:** We need to find the perimeter of a right-angled triangle with sides 8 cm, 2 cm, and 15 cm given. 2. **Identify the sides:** The triangle has a vertical side of 8 cm, a small horizontal segment of 2 cm, and a longer horizontal side of 15 cm. The right angle is between the 8 cm and 2 cm sides. 3. **Understand the triangle:** The 2 cm and 8 cm sides form the right angle, so the hypotenuse is the side opposite the right angle. The 15 cm side is the hypotenuse. 4. **Check if the sides form a right triangle:** Use Pythagoras' theorem: $$a^2 + b^2 = c^2$$ where $a=2$, $b=8$, and $c=15$. Calculate: $$2^2 + 8^2 = 4 + 64 = 68$$ $$15^2 = 225$$ Since $68 \neq 225$, the 15 cm side is not the hypotenuse of the triangle formed by 2 cm and 8 cm sides. 5. **Interpret the figure:** The 15 cm side is the total horizontal length, which includes the 2 cm segment plus the base of the right triangle. So the base of the right triangle is $15 - 2 = 13$ cm. 6. **Calculate the hypotenuse:** Now the right triangle has legs 8 cm and 13 cm. Use Pythagoras' theorem: $$c = \sqrt{8^2 + 13^2} = \sqrt{64 + 169} = \sqrt{233}$$ 7. **Calculate the value:** $$\sqrt{233} \approx 15.2643$$ 8. **Calculate the perimeter:** The perimeter is the sum of all sides: $$8 + 13 + 15.2643 = 36.2643$$ 9. **Round to 1 decimal place:** $$36.3$$ **Final answer:** The perimeter of the triangle is $36.3$ cm.