Explanation:

- First, calculate the area of the first triangle using the formula:

$$ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $$

$$ \text{Area} = \frac{1}{2} \times 8.5 \, \text{cm} \times 14 \, \text{cm} = 59.5 \, \text{cm}^2 $$

- The area of the second triangle is double that of the first triangle:

$$ \text{Area of second triangle} = 2 \times 59.5 \, \text{cm}^2 = 119 \, \text{cm}^2 $$

- Use the area formula to find the height of the second triangle with base 14 cm:

$$ 119 = \frac{1}{2} \times 14 \, \text{cm} \times \text{height} $$

$$ 119 = 7 \times \text{height} $$

$$ \text{Height} = \frac{119}{7} = 17 \, \text{cm} $$

- Therefore:

- Option 1: 17 cm is the correct option.