To solve this problem, we need to first determine the scale ratio based on the length of the classroom and the scale drawing. After finding the scale, we can use it to determine the width in the scale drawing and finally compute the perimeter of the rectangle.

Step-by-Step Solution:

1. Find the scale factor:

   • The actual length of the classroom is 30 feet.
   • The length in the scale drawing is 10 inches.
   • The scale factor is: $\text{Scale factor} = \frac{\text{length in scale drawing}}{\text{actual length}} = \frac{10 \text{ inches}}{30 \text{ feet}}.$
   • Since 1 foot = 12 inches, we convert 30 feet to inches: $30 \text{ feet} = 30 \times 12 = 360 \text{ inches}.$
   • Now, calculate the scale factor: $\text{Scale factor} = \frac{10}{360} = \frac{1}{36}.$

2. Calculate the width in the scale drawing:

   • The actual width of the classroom is 33 feet.
   • Convert 33 feet to inches: $33 \text{ feet} = 33 \times 12 = 396 \text{ inches}.$
   • Now, use the scale factor to find the width in the scale drawing: $\text{Width in scale drawing} = \frac{1}{36} \times 396 = 11 \text{ inches}.$

3. Find the perimeter of the scale drawing:

   • The perimeter $P$ of a rectangle is given by the formula: $P = 2 \times (\text{length} + \text{width}).$
   • In the scale drawing, the length is 10 inches and the width is 11 inches, so: $P = 2 \times (10 + 11) = 2 \times 21 = 42 \text{ inches}.$

Thus, the perimeter of the floor in the scale drawing is 42 inches.

Would you like more details or have any questions about this solution?

Related Questions:

1. What is the area of the classroom in both actual and scale dimensions?
2. How would the perimeter change if the classroom was square instead of rectangular?
3. What if the scale drawing's width was given instead of the length? How would the problem change?
4. Can you solve for the perimeter in feet if given the scale factor in another unit?
5. How would a different scale factor (e.g., $\frac{1}{24}$) affect the final result?

Tip:

Always convert all units to the same measurement system (e.g., inches to inches) before solving scale problems to avoid errors in calculations.