Question 11

The height of the triangle is 8 centimeters.

To find the height \( h \) of the triangle, we use the area formula for triangles, which is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Given the area is 24 square centimeters, we can rearrange the formula to solve for height.

A) 9

Option A is incorrect because if the height were 9 centimeters, the area calculation would yield a much larger area than 24 square centimeters, assuming a reasonable base. For instance, with a base of 4 cm, the area would be \( \frac{1}{2} \times 4 \times 9 = 18 \) which is less than 24, indicating that this height cannot correspond to the given area.

B) 4

Option B is also incorrect. If the height were 4 centimeters, the area would again not match the given area. For a base of 12 cm, the area would be calculated as \( \frac{1}{2} \times 12 \times 4 = 24 \), but if the base were smaller, the area would be less than 24, showing that this height does not necessarily yield the required area with typical base measurements.

C) 8

Option C is correct. By using the height of 8 centimeters, and assuming a base of 6 centimeters, we can find that the area equals \( \frac{1}{2} \times 6 \times 8 = 24 \) square centimeters. This matches the provided area, confirming that 8 centimeters is the correct height for the triangle.

D) 2

Option D is incorrect. If the height were 2 centimeters, even with a larger base, the resulting area would not reach 24 square centimeters. For instance, with a base of 24 cm, the area would be \( \frac{1}{2} \times 24 \times 2 = 24 \), but it would be impractical for typical triangle dimensions, which typically wouldn't match the typical base-height ratios.

Conclusion

The correct height of 8 centimeters is verified through the area calculation, which matches the given area of 24 square centimeters when appropriate base lengths are considered. Options A, B, and D either yield insufficient area or unrealistic dimensions, confirming that option C is the only viable choice.