Question

the rectangular floor of a classroom is 28 feet in length and 38 feet in width. a scale drawing of the floor has a length of 14 inches. what is the area, in square inches, of the floor in the scale drawing?

Explanation:

Step1: Find the scale factor

The actual length is 28 feet = \(28 \times 12 = 336\) inches. The scaled length is 14 inches.
Scale factor \(k = \frac{\text{scaled length}}{\text{actual length}} = \frac{14}{336} = \frac{1}{24}\)

Step2: Find scaled width

Actual width is 38 feet = \(38 \times 12 = 456\) inches.
Scaled width \(= 456 \times \frac{1}{24} = 19\) inches

Step3: Calculate scaled area

Area = scaled length × scaled width
\(14 \times 19 = 266\)

Answer:

266 square inches