The scale ratio of a point A to another point B is the division of the length of B by the length of A. The area of the room is approximately 266.67 square feet.
Given that:
[tex]Scale = 1:40[/tex]
[tex]l = 6in[/tex] --- length of rectangle
[tex]w = 4in[/tex] --- width of rectangle
Divide by 12 to convert the dimensions to feet
[tex]l = \frac{6}{12}ft[/tex]
[tex]w=\frac{4}{12}ft[/tex]
[tex]Scale = 1:40[/tex] means that the dimension of the room is 40 times the dimension of the rectangle.
So, we have:
[tex]Length = \frac{6}{12}ft * 40 = 20ft[/tex]
[tex]Width = \frac{4}{12}ft * 40 = \frac{40}{3}ft[/tex]
The area of the room is:
[tex]Area = Length * Width[/tex]
So, we have:
[tex]Area = 20ft * \frac{40}{3}ft[/tex]
[tex]Area = \frac{800}{3}ft^2[/tex]
[tex]Area = 266.67ft^2[/tex]
The area of the room is 266.67 square feet
Read more about scale ratios at:
https://brainly.com/question/16713785
