Question

The models of two apartments are shown with the scales used to create them. Each gridline represents 1 centimeter

City Apartment
Scale: 3ft/1cm
Suburban Apartment
Scale: 7.5ft/2cm

Which statement is true?
A The scale factor from the suburban apartment to the city apartment is 1.5ft/1cm.
B The area of the city apartment is approximately equal to the area of the suburban apartment.
C The area of the suburban apartment is 108 square feet larger than the area of the city apartment.
D The area of the city apartment is 112.5 square feet smaller than the area of the suburban apartment.

Answer 1

The scale factor from the suburban apartment to the city apartment is 1.5ft/1cm.

Step-by-step explanation:

To determine which statement is true, we need to compare the scales of the two apartment models. The scale of the city apartment is 3ft/1cm, which means that 3 feet of the actual apartment is represented by 1 centimeter in the model. The scale of the suburban apartment is 7.5ft/2cm, which means that 7.5 feet of the actual apartment is represented by 2 centimeters in the model.

By comparing the two scales, we can see that the scale factor from the suburban apartment to the city apartment is 3.75ft/1cm. This is obtained by dividing the scale factor of the suburban apartment by the scale factor of the city apartment (7.5/2 = 3.75/1).

Therefore, the correct answer is Option A: The scale factor from the suburban apartment to the city apartment is 1.5ft/1cm.