The rectangular floor of a classroom is 26 feet in length and 36 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?

To find the perimeter of the floor in the scale drawing, we need to first determine the scale factor between the actual dimensions and the dimensions in the scale drawing.

Given:

Actual length = 26 ft = 26 ft × 12 in/ft = 312 in

Actual width = 36 ft = 36 ft × 12 in/ft = 432 in

Scale length = 13 in

We can find the scale factor by comparing the actual length to the length in the scale drawing:

[tex] \begin{aligned} \textsf{Scale factor} & = \dfrac{\textsf{Length in scale drawing}}{\textsf{Actual length}} \\\\ & = \dfrac{13 \textsf{ in }}{ 312 \textsf{ in}} \\\\ & = \dfrac{1}{24} \end{aligned} [/tex]

Now we can use this scale factor to find the width in the scale drawing:

[tex] \begin{aligned} \textsf{Scale width} & = \textsf{Scale factor} \times \textsf{Actual width} \\\\ & = \dfrac{1}{24 }\times 432 \textsf{ in } \\\\ & = 18 \textsf{ in} \end{aligned} [/tex]

The perimeter in the scale drawing is:

[tex] \begin{aligned} \textsf{Perimeter} & = 2 \times (\textsf{Scale length} + \textsf{Scale width}) \\\\ & = 2 \times (13 \textsf{ in} + 18 \textsf{ in}) \\\\ & = 2 \times 31 \textsf{ in } \\\\ & = 62 \textsf{ in} \end{aligned} [/tex]

So, the perimeter of the floor in the scale drawing is 62 in.