Question

3 a blueprint for a rectangular warehouse has a length of 18 inches and a width of 10 inches. it uses a scale of 1 inch for every 20 feet.
a. what is the actual area of the warehouse in square feet? how do you know?
4 diego drew a scaled copy of polygon a and labeled it polygon b.
if the area of polygon a is 7 square units, what scale factor did diego apply to polygon a to create polygon b? explain or show how you know.
(from unit 1, lesson 12.)

Explanation:

Step1: Calculate the actual length and width

The scale is \(1\) inch for every \(20\) feet.
The length on the blueprint is \(18\) inches. Let the actual length be \(l\). Using the proportion \(\frac{1}{20}=\frac{18}{l}\), we get \(l = 18\times20=360\) feet.
The width on the blueprint is \(10\) inches. Let the actual width be \(w\). Using the proportion \(\frac{1}{20}=\frac{10}{w}\), we get \(w = 10\times20 = 200\) feet.

Step2: Calculate the area

The area of a rectangle \(A=l\times w\). Substitute \(l = 360\) and \(w = 200\) into the formula. So \(A=360\times200 = 72000\) square feet.

Answer:

The actual area of the warehouse is \(72000\) square feet. We know this by first using the scale factor to convert the blueprint dimensions (length \(18\) inches and width \(10\) inches) to actual dimensions (\(360\) feet and \(200\) feet respectively) using proportion \(\frac{\text{blueprint dimension}}{\text{actual dimension}}=\frac{1}{20}\), and then using the formula for the area of a rectangle \(A = l\times w\).