Question

an architect makes a scale model of a building where one inch in the model represents 10 feet. which statement is true? o a) the area covered by the building is 144 times the area covered by the model. o b) the area covered by the building is 14,400 times the area covered by the model. o c) the area covered by the building is 12 times the area covered by the model. o d) the area covered by the building is 120 times the area covered by the model.

Explanation:

Step1: Convert feet to inches

Since 1 foot = 12 inches, 10 feet = 10×12 = 120 inches. The linear - scale factor from the model to the building is 120 (1 inch in model represents 120 inches in real - life).

Step2: Recall the relationship between linear and area scale factors

For similar figures, if the linear - scale factor is \(k\), the area - scale factor is \(k^{2}\). Here, \(k = 120\), so the area - scale factor is \(k^{2}=120^{2}=14400\).

Answer:

B. The area covered by the building is 14,400 times the area covered by the model.