Question

a commercial real estate developer creates a scale drawing of a commercial property that he hopes to sell. the ratio of the area of the drawing to the actual area of the commercial property is 1 ft²:900 ft². the developer hopes to sell the commercial space for $1,800,000, which would be equivalent to $1000 per 1 square foot (ft²) of the propertys area. to the nearest square foot, what is the area of the scale drawing?

Explanation:

Step1: Find the actual area of the commercial property

The developer hopes to sell the commercial space for $\$1,800,000$ at a rate of $\$1000$ per square - foot.
Let the actual area of the property be $A$. Using the formula $\text{Total Price}=\text{Rate per unit area}\times\text{Area}$, we have $1800000 = 1000\times A$.
Solving for $A$, we get $A=\frac{1800000}{1000}=1800\ \text{ft}^2$.

Step2: Use the ratio of areas to find the area of the scale - drawing

The ratio of the area of the drawing to the actual area is $1:900$. Let the area of the drawing be $x$.
We have the proportion $\frac{x}{1800}=\frac{1}{900}$.
Cross - multiplying gives $900x = 1800$.
Solving for $x$, we get $x=\frac{1800}{900}=2\ \text{ft}^2$.

Answer:

$2$