The rectangular floor of a classroom is $32$ feet in length and $26$ feet in width. A scale drawing of the floor has a length of $16$ 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

32

feet in length and

26

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

16

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 $32$ feet, and the actual width is $26$ feet. The scale drawing has a length of $16$ 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. $\newline$ The scale factor is the ratio of the length in the scale drawing to the actual length. Since $1$ foot is equal to $12$ inches, we first convert the actual length from feet to inches: $32$ feet $\times 12$ inches/foot $= 384$ inches. Now we can find the scale factor: Scale factor $= \frac{\text{length in scale drawing}}{\text{actual length in inches}} = \frac{16 \text{ inches}}{384 \text{ inches}}$ .
Simplify scale factor: Simplify the scale factor. Simplify the scale factor by dividing both the numerator and the denominator by the greatest common divisor, which is $16$ in this case: Scale factor = $\frac{16 \text{ inches}}{384 \text{ inches}} = \frac{1}{24}$ .
Calculate width in drawing: Calculate the width in the scale drawing using the scale factor. $\newline$ Now we use the scale factor to find the width in the scale drawing. First, convert the actual width from feet to inches: $26 \text{ feet} \times 12 \text{ inches/foot} = 312 \text{ inches}$ . Then multiply the actual width in inches by the scale factor: Width in scale drawing = $312 \text{ inches} \times (1 / 24)$ .
Simplify width calculation: Simplify the calculation to find the width in the scale drawing. Width in scale drawing = $312 \text{ inches} \times \left(\frac{1}{24}\right) = 13 \text{ inches}.$
Calculate perimeter: Calculate the perimeter of the scale drawing. $\newline$ The perimeter of a rectangle is the sum of all its sides. In the scale drawing, the length is $16$ inches, and the width is $13$ inches. So, the perimeter is $2$ times the sum of the length and width: Perimeter = $2 \times (\text{length} + \text{width}) = 2 \times (16 \text{ inches} + 13 \text{ inches})$ .
Simplify perimeter calculation: Simplify the calculation to find the perimeter of the scale drawing. $\newline$ Perimeter = $2 \times (16 \text{ inches} + 13 \text{ inches}) = 2 \times 29 \text{ inches} = 58 \text{ inches}.$