Certainly! Let’s walk through each step in solving this problem. We are given the dimensions in the architectural drawing and need to convert those dimensions to the actual size of the bedroom using the given scale.
### Step-by-step solution:
1. Understand the Scale:
The scale provided is [tex]\( \frac{1}{4} \)[/tex] inch = 1 foot. This means that for every [tex]\( \frac{1}{4} \)[/tex] inch on the drawing, it represents 1 foot in reality. Therefore, 1 inch on the drawing represents 4 feet in reality.
2. Convert Drawing Dimensions to Decimal Form:
The dimensions provided in inches need to be interpreted correctly.
- Length: [tex]\( 64 \frac{3}{16} \)[/tex] inches.
To convert [tex]\( 64 \frac{3}{16} \)[/tex] to a decimal:
[tex]\[
64 + \frac{3}{16} = 64 + 0.1875 = 64.1875 \text{ inches}
\][/tex]
- Width: [tex]\( 4 \frac{1}{2}^{\frac{1}{2}} \)[/tex] inches.
To convert [tex]\( 4 \frac{1}{2}^{\frac{1}{2}} \)[/tex] to a decimal:
[tex]\[
4 + \frac{1}{2} + \left( \frac{1}{2} \right)^2 = 4 + 0.5 + 0.25 = 4.75 \text{ inches}
\][/tex]
3. Apply the Scale:
Next, we multiply the drawing measurements by the conversion factor (4) to get the actual dimensions.
- Actual Length:
[tex]\[
64.1875 \text{ inches} \times 4 = 256.75 \text{ feet}
\][/tex]
- Actual Width:
[tex]\[
4.75 \text{ inches} \times 4 = 19.0 \text{ feet}
\][/tex]
4. Determine the Closest Answer:
Now that we have the actual measurements:
- Length: 256.75 feet
- Width: 19.0 feet
Comparing these dimensions with the provided options:
- Option A: 11 ft by 27 ft
- Option B: 72 in. by 108 in. (Note: This is in inches, whereas all other units are in feet.)
- Option C: 111 ft by 81 ft
- Option D: 0 ft by 13.5 ft
Clearly none of these options exactly match the calculated dimensions.
But looking at the provided options, it might reflect a multiple choice error or typo in the problem.
However, based on the exact results for the dimensions using the scale provided, the size of the bedroom in the drawing correctly translates to:
[tex]\[ \text{256.75 ft by 19.0 ft} \][/tex]
