The rectangular floor of a classroom is $27$ feet in length and $21$ feet in width. A scale drawing of the floor has a length of $9$ inches. What is the perimeter, in inches, of the floor in the scale drawing? $\newline$ Answer: $\square$ in.

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Q. The rectangular floor of a classroom is

27

feet in length and

21

feet in width. A scale drawing of the floor has a length of

9

inches. What is the perimeter, in inches, of the floor in the scale drawing?

\newline

Answer:

\square

in.

Identify Dimensions and Scale: Identify the actual dimensions of the classroom floor and the scale used in the drawing. $\newline$ The actual length of the classroom floor is $27$ feet, and the actual width is $21$ feet. The scale drawing has a length of $9$ inches. We need to find the scale factor to use it for finding the width in the scale drawing and then calculate the perimeter.
Calculate Scale Factor: Calculate the scale factor. $\newline$ Since the actual length is $27$ feet and the scale drawing length is $9$ inches, we convert the actual length to inches (since $1$ foot $= 12$ inches) and then find the scale factor. $\newline$ Actual length in inches $= 27$ feet $\times 12$ inches/foot $= 324$ inches. $\newline$ Scale factor $=$ Scale drawing length / Actual length in inches $= 9$ inches $/ 324$ inches. $\newline$ Scale factor $9$ $0$ .
Calculate Width in Drawing: Calculate the width in the scale drawing using the scale factor. $\newline$ Actual width in inches = $21 \text{ feet} \times 12 \text{ inches/foot} = 252 \text{ inches}$ . $\newline$ Width in scale drawing = Actual width in inches $\times$ Scale factor = $252 \text{ inches} \times \frac{1}{36}$ . $\newline$ Width in scale drawing = $7 \text{ inches}$ .
Calculate Perimeter: Calculate the perimeter of the scale drawing. $\newline$ Perimeter of a rectangle = $2 \times (\text{length} + \text{width})$ . $\newline$ Perimeter in scale drawing = $2 \times (9 \text{ inches} + 7 \text{ inches}) = 2 \times 16 \text{ inches} = 32 \text{ inches}$ .
Verify Perimeter Calculation: Verify that the perimeter calculation is correct and matches the scale. $\newline$ The perimeter of the actual classroom floor is $2 \times (27 \text{ feet} + 21 \text{ feet}) = 2 \times 48 \text{ feet} = 96 \text{ feet}$ . $\newline$ Converting the actual perimeter to inches: $96 \text{ feet} \times 12 \text{ inches/foot} = 1152 \text{ inches}$ . $\newline$ Since the scale factor is $1/36$ , the perimeter in the scale drawing should be $1152 \text{ inches} \times 1/36 = 32 \text{ inches}$ , which matches our calculation.