Question

a rectangular room has a length of 12 feet and a width of 15 feet. a contractor creates a blueprint of the room using a scale factor of \\(\frac{1}{6}\\). here is the table from the previous screen. \\\

$$\begin{array}{|c|c|}\\hline \\text{length (ft)} & \\text{width (ft)} \\\\ \\hline 2 & 2.5 \\\\ \\hline \\end{array}$$

\\ how does the area of the actual room compare to the area on the blueprint?

Explanation:

Step1: Calculate actual area

Actual length \( l = 12 \) ft, width \( w = 15 \) ft. Area \( A_{actual} = l \times w = 12 \times 15 = 180 \) sq ft.

Step2: Calculate blueprint area

Blueprint length \( l' = 2 \) ft, width \( w' = 2.5 \) ft. Area \( A_{blueprint} = l' \times w' = 2 \times 2.5 = 5 \) sq ft.

Step3: Find the ratio

Ratio \( = \frac{A_{actual}}{A_{blueprint}} = \frac{180}{5} = 36 \). Or, since scale factor is \( \frac{1}{6} \), area scale factor is \( (\frac{1}{6})^2=\frac{1}{36} \), so actual area is \( 36 \) times blueprint area.

Answer:

The area of the actual room is 36 times the area on the blueprint.