The triangle shown in the diagram has an area of 24 square centimeters. What is h, the height in centimeters, of the triangle?

Rationale

The height of the triangle is 8 centimeters.

To find the height of the triangle, we can use the formula for the area of a triangle, which is Area = 0.5 × base × height. Given that the area is 24 square centimeters, we can rearrange the formula to solve for height when the base is known.

A (9) YOUR ANSWER

If the height were 9 centimeters, we would need to know the base to verify this choice. However, plugging this value into the area formula (Area = 0.5 × base × 9) would yield an area greater than 24 square centimeters for any reasonable base length, thus making this choice incorrect.

B (4) YOUR ANSWER

Using 4 centimeters as the height, the area calculation would need a base of 12 centimeters (Area = 0.5 × 12 × 4 = 24). While this gives the correct area, it does not represent the height that yields the area directly from the given information, making this choice misleading.

C (8) CORRECT

Using 8 centimeters as the height, we can find the base needed to achieve the area of 24 square centimeters. If we set the base to 6 centimeters (Area = 0.5 × 6 × 8 = 24), this satisfies the area requirement perfectly, confirming that 8 centimeters is indeed the correct height.

D (2) YOUR ANSWER

If the height were 2 centimeters, the area would only be 24 square centimeters if the base were 24 centimeters (Area = 0.5 × 24 × 2 = 24). While this is mathematically valid, it does not provide a height that is representative of typical triangle dimensions, and thus fails to capture the height in a relevant context.

Conclusion

Through the application of the area formula for triangles, we can verify that the height of 8 centimeters is the only value that directly results in the area of 24 square centimeters when using reasonable dimensions for the base. The other options fail either to yield the correct area or do not represent a typical height corresponding to a triangle's dimensions, making 8 centimeters the definitive solution.

The triangle shown in the diagram has an area of 24 square centimeters. What is h, the height in centimeters, of the triangle?

The height of the triangle is 8 centimeters.

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