Question

the rectangular floor of a classroom is 33 feet in length and 24 feet in width. a scale drawing of the floor has a length of 11 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 33 feet and the length in the scale - drawing is 11 inches. Since 1 foot = 12 inches, 33 feet = 33×12 = 396 inches. The scale factor $k$ for length is $\frac{11}{396}=\frac{1}{36}$.

Step2: Find the width in the scale - drawing

The actual width is 24 feet, which is 24×12 = 288 inches. The width in the scale - drawing $w$ is $288\times\frac{1}{36}=8$ inches.

Step3: Calculate the area of the scale - drawing

The area $A$ of a rectangle is $A = l\times w$. Here, $l = 11$ inches and $w = 8$ inches. So $A=11\times8 = 88$ square inches.

Answer:

88