The rectangular floor of a classroom is $26$ feet in length and $24$ feet in width. A scale drawing of the floor has a length of $13$ 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

26

feet in length and

24

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

13

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

\newline

Answer:

\square

in.

Identify Dimensions: Identify the actual dimensions of the classroom floor and the scale drawing length. $\newline$ The actual length of the classroom floor is $26$ feet, and the actual width is $24$ feet. The scale drawing length is $13$ inches.
Determine Scale Factor: Determine the scale factor between the actual floor dimensions and the scale drawing. Since the actual length is $26$ feet and the scale drawing length is $13$ inches, we need to convert feet to inches to find the scale factor. There are $12$ inches in a foot, so the actual length in inches is $26$ feet $\times 12$ inches/foot $= 312$ inches. The scale factor is the scale drawing length divided by the actual length in inches, which is $13$ inches $/$ $312$ inches.
Calculate Factor: Calculate the scale factor. $\newline$ The scale factor is $13$ inches / $312$ inches = $\frac{1}{24}$ .
Determine Width: Determine the width of the classroom floor in the scale drawing using the scale factor. $\newline$ The actual width is $24$ feet, which is $24$ feet $\times 12$ inches/foot $= 288$ inches. Using the scale factor of $1/24$ , the width in the scale drawing is $288$ inches $\times (1/24) = 12$ inches.
Calculate Perimeter: Calculate the perimeter of the classroom floor in the scale drawing. $\newline$ The perimeter of a rectangle is $2$ times the length plus $2$ times the width. The length in the scale drawing is $13$ inches, and the width we've calculated is $12$ inches. So, the perimeter is $2 \times 13$ inches $+ 2 \times 12$ inches $= 26$ inches $+ 24$ inches $= 50$ inches.