Question

An architect created the blueprints for the Chin's house. The scale factor is 1 inch: 40 inches. The length and width of the living room on the blueprint are 4 inches and 8 inches respectively. WHat is the area of the actual living room?

Answer 1

The measurements for the actual room are, in inches, 160 x 320

Explanation:

If you want the computed area, then multiply those numbers together since A=bh. I assumed you were just looking for the measurements of the actual room. Set up a ratio for the scale first, the model info in the numerator and the actual room info in the denominator:

`(m)/(a): (1)/(40)`

Here, the m is the model on paper and the a is the actual room. So if the length of the room on paper is 4 inches, that will go on top with the model stuff and we will solve for the missing equivalent length of the actual room:

`(m)/(a) :(1)/(40) =(4)/(x)`

Cross multiply to get that the length of the actual room is 160 inches long. Divide by 12 if you need that number in feet.

Doing the same with the width:

`(m)/(a) :(1)/(40)=(8)/(y)`

Cross multiply to get that the width of the actual room is 320 inches. Again, if you need that in feet, divide by 12.

Answer 2

Step 1: Find the area of the living room on the blueprint with the formula Area = length x height

A = 4 x 8

A = 32

Step 2: We now know that the area of the living room on the blueprint is 32 inches, but we have to convert it into the actual answer. To do this multiply 32 by 40 (you have to do this because 1 inch is 40 inch in reality meaning that each inch in the 32 inches is times 40 <<< Does that make sense?), so...

40 x 32 = 1,280

Hope this helped!