Question

scale: 1 inch : 4 feet. what is the actual area of the living room? blueprint area 15 in². actual area? ft²

Explanation:

Step1: Find the scale - factor for area

The linear scale is 1 inch : 4 feet. For area, the scale - factor is the square of the linear scale - factor. Since the linear scale factor is $k = 4$ (because 1 inch represents 4 feet), the area scale - factor is $k^{2}=4^{2}=16$.

Step2: Calculate the actual area

We know the blueprint area $A_{b}=15$ in². To find the actual area $A_{a}$, we multiply the blueprint area by the area scale - factor. So $A_{a}=A_{b}\times k^{2}$. Substituting the values, we get $A_{a}=15\times16 = 240$ ft².

Answer:

240 ft²