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This problem involves using similar triangles to determine the height of the building. The shadow of the building and the shadow of the man form two right triangles, both of which are similar because they are created by the same light source.

Given:
- The man's height is 6 feet, and his shadow is 2 feet long.
- The building's shadow is 24 feet long, and we need to find the building's height.

Since the triangles are similar, the ratios of corresponding sides are equal:

\[
\frac{\text{Building's height}}{\text{Building's shadow}} = \frac{\text{Man's height}}{\text{Man's shadow}}
\]

Substituting the known values:

\[
\frac{\text{Building's height}}{24} = \frac{6}{2}
\]

Solving for the building's height:

\[
\frac{\text{Building's height}}{24} = 3 \quad \Rightarrow \quad \text{Building's height} = 3 \times 24 = 72 \text{ feet}
\]

Therefore, the correct height of the building is **72 feet**, and the correct answer is **D**.

Would you like further details or explanations?

Here are 5 related questions to expand on this concept:
1. How would the problem change if the building’s shadow was shorter?
2. What is the mathematical definition of similar triangles?
3. Can we solve this using a different method, such as trigonometry?
4. How do we know the triangles are similar in this problem?
5. What other real-world situations involve similar triangles?

**Tip:** In any problem involving shadows and heights, if the light source is the same, similar triangles will always form!

A building casts a shadow that is 24 feet long. At the same time and nearby, a man that is 6 feet tall casts a shadow that is 2 feet long. How tall is the building?

Learn how to calculate the height of a building using similar triangles. Given that a building casts a shadow of 24 feet and a man 6 feet tall casts a shadow of 2 feet, apply proportions to solve this real-world geometry problem. Suitable for Grades 6-8.

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