Step 1: Identify the given information for the first triangle. The base of the first triangle is $b_1 = 14$ cm. The area of the first triangle is $A_1 = 98 \text{ cm}^2$. Step 2: Calculate the area of the second triangle. The problem states that the area of the second triangle ($A_2$) is double the area of the first triangle ($A_1$). $$A_2 = 2 \times A_1$$ $$A_2 = 2 \times 98 \text{ cm}^2$$ $$A_2 = 196 \text{ cm}^2$$ Step 3: Identify the given information for the second triangle. The base of the second triangle is $b_2 = 14$ cm (same as the first triangle). The area of the second triangle is $A_2 = 196 \text{ cm}^2$. We need to find the height of the second triangle, $h_2$. Step 4: Use the formula for the area of a triangle to find the height of the second triangle. The formula for the area of a triangle is: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ For the second triangle: $$A_2 = \frac{1}{2} \times b_2 \times h_2$$ Substitute the known values: $$196 \text{ cm}^2 = \frac{1}{2} \times 14 \text{ cm} \times h_2$$ $$196 \text{ cm}^2 = 7 \text{ cm} \times h_2$$ Now, solve for $h_2$: $$h_2 = \frac{196 \text{ cm}^2}{7 \text{ cm}}$$ $$h_2 = 28 \text{ cm}$$ The height of the second triangle is 28 cm. Comparing this with the given options: A. 21 cm B. 7 cm C. 28 cm D. 14 cm The correct option is C. The final answer is $\boxed{\text{28 cm}}$.