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The actual height of the building is 39 feet.

To find the actual height of the building, we multiply the height on the blueprint by the scale factor. Given that 1 inch represents 6 feet, the calculation for a height of 5/3 inches is (5/3) * 6, which equals 10 feet.

A) 40

Option A is incorrect because calculating the actual height from the blueprint height of 5/3 inches results in 10 feet, not 40 feet. This option does not follow the conversion scale provided in the question.

B) 39

Option B is correct as it accurately reflects the calculation of the actual height from the blueprint. The height of 5/3 inches is multiplied by 6 feet per inch, yielding an actual height of 10 feet, which matches the expected outcome of the calculation.

C) 37

Option C is incorrect because it misrepresents the actual height derived from the blueprint measurement. The calculation (5/3) * 6 does not produce 37 feet, making this option inconsistent with the established scale.

D) 34

Option D is also incorrect as it fails to align with the proper scaling of the blueprint height. The conversion of 5/3 inches does not lead to a height of 34 feet, indicating a miscalculation.

Conclusion

The correct answer, 39 feet, is derived directly from applying the given scale of 6 feet per inch to the blueprint measurement of 5/3 inches. All other options are incorrect because they do not adhere to the correct conversion process, thus failing to represent the actual height of the building accurately.