Question

1. Your family has decided to build a home. The architect has prepared blue prints so thatyou can have a scale drawing of the house which will allow you to make decisions of thefinishes. On the blue print, your room is 3.7 inches by 4.1 inches.a. What is the actual square footage of your room if the scale for the prints is 50:1?Show all of the conversion factors to determine the solution and keep in mind that theresult needs to be in ft2?.

Answer 1

1) In this problem, we need to convert the scale to get the area.

2) So, let's begin with the area in the blueprint. Note that the area is an area of a rectangle, so we can write out the following:

`\begin{gathered} 3.7^(\doubleprime)/12=0.308333ft \\ 4.1/12=0.341667ft \\ A=0.308333*0.341667 \\ A=0.10534ft^(2) \end{gathered}`

Notice that we converted from inches to feet before calculating the area of that room in the blueprint.

2.2)

`\begin{gathered} S^2=(a)/(A) \\ S^2=(0.10534)/(A) \\ ((1)/(50))^2=(0.10534)/(A) \\ (1)/(2500)=(0.10534)/(A) \\ A=263.35ft^(2) \end{gathered}`