Explanation:

- The area of a triangle with sides 13 cm, 14 cm, and 15 cm can be calculated using Heron's formula.

- First, find the semi-perimeter: \( s = \frac{13 + 14 + 15}{2} = 21 \) cm.

- Use Heron's formula to find the area:

$$ \text{Area} = \sqrt{s(s-13)(s-14)(s-15)} = \sqrt{21 \times 8 \times 7 \times 6} = \sqrt{7056} = 84 \text{ cm}^2 $$

- The smallest altitude corresponds to the largest side, which is 15 cm.

- Use the formula for altitude:

$$ \text{Altitude} = \frac{\text{Area} \times 2}{\text{base}} = \frac{84 \times 2}{15} = 11.2 \text{ cm} $$

- Based on calculations, the length of the smallest altitude of the triangle is 11.2 cm.

Option 2: 11.2 cm