Final answer:
The height of the scale model is solved by setting up a proportion between the real building's dimensions and the model's width. After cross-multiplying and simplifying, we find that the model's height is 6 inches.
So option (D) is the correct answer.
Step-by-step explanation:
To find the height of the scale model of a building, we can set up a proportion based on the given dimensions of the real building and the width of the scale model. The building is 24 feet tall and 40 feet wide, and the scale model is 10 inches wide. To solve for the height of the scale model, we use the following proportion:
(height of real building) / (width of real building) = (height of model) / (width of model)
24 feet / 40 feet = (model's height in inches) / 10 inches
Now, cross-multiplying, we have:
24 feet * 10 inches = (model's height in inches) * 40 feet
240 feet-inches = 40 feet × (model's height in inches)
Finally, divide both sides by 40 feet to solve for the model's height:
6 inches = (model's height in inches)
Hence, the model's height is 6 inches, which corresponds to option A.