1. **State the problem:** We have a triangle with side lengths in the ratio 2 : 6 : 7, and the longest side is 24.5 cm. We need to find the perimeter of the triangle. 2. **Understand the ratio:** The sides can be represented as $2x$, $6x$, and $7x$, where $x$ is a common multiplier. 3. **Use the given longest side:** Since the longest side corresponds to the ratio 7, we set: $$7x = 24.5$$ 4. **Solve for $x$:** $$x = \frac{24.5}{7} = 3.5$$ 5. **Find the other sides:** - Second side: $6x = 6 \times 3.5 = 21$ - First side: $2x = 2 \times 3.5 = 7$ 6. **Calculate the perimeter:** $$\text{Perimeter} = 7 + 21 + 24.5 = 52.5$$ 7. **Answer:** The perimeter of the triangle is **52.5 cm**.