Question

Mario constructs a scale model of a building with a rectangular base. His model is 4.2 inches in length and 2 inches in width. The scale of the model is 1 inch = 15 feet What is the actual area, in square feet, of the base of the building?

Answer 1

First let's use two rules of three to determine the actual dimensions of the building.

For the length, we have:

`\begin{gathered} 1\text{ inch}\to15\text{ feet} \\ 4.2\text{ inches}\to x\text{ feet} \\ \\ (1)/(4.2)=(15)/(x) \\ x=15\cdot4.2=63 \end{gathered}`

For the width:

`\begin{gathered} 1\text{ inch}\to15\text{ feet} \\ 2\text{ inches}\to x\text{ feet} \\ \\ (1)/(2)=(15)/(x) \\ x=15\cdot2=30 \end{gathered}`

Now, calculating the area of the building base, we have:

`\text{Area}=63\cdot30=1890\text{ ft2}`

So the area of the building base is 1890 ft².