Question

an architect drew the blueprint for a new office building. he used a scale in which 1 inch represents 7.5 feet. the floor of an office in the building will have actual dimensions of 20 feet by 19 feet. what will be the dimensions on the blueprint?

a. 2.67 inches by 2.53 inches
b. 27.5 inches by 26.5 inches
c. 150 inches by 142.5 inches
d. 12.5 inches by 11.5 inches

Explanation:

Identify the scale factor and actual dimensions

The scale is given as \(1\text{ inch} = 7.5\text{ feet}\).
The actual dimensions of the office floor are \(20\text{ feet}\) by \(19\text{ feet}\).

Calculate the blueprint dimensions

To find the dimensions on the blueprint, divide each actual dimension by the scale factor of \(7.5\text{ feet per inch}\):

$$ \text{Width on blueprint} = \frac{20}{7.5} \approx 2.67\text{ inches} $$

$$ \text{Length on blueprint} = \frac{19}{7.5} \approx 2.53\text{ inches} $$

Match with the given options

The calculated dimensions are \(2.67\text{ inches}\) by \(2.53\text{ inches}\), which corresponds to option A.

Answer:

• A. 2.67 inches by 2.53 inches (Correct answer)
• B. 27.5 inches by 26.5 inches
• C. 150 inches by 142.5 inches
• D. 12.5 inches by 11.5 inches