To determine the actual size of the bedroom from the measurements given on the architectural drawing, we need to understand the scale provided and make the necessary conversions.
The scale is given as [tex]\( \frac{1}{4}" = 1' \)[/tex]. This means that for every quarter inch on the drawing, the real-life size is 1 foot. Therefore, 1 inch on the drawing represents 4 feet in actual size.
### Step-by-Step Solution:
1. Understand the Dimensions on the Drawing:
The bedroom measures [tex]\(3 \frac{1}{2}"\)[/tex] by [tex]\(5 \frac{1}{4}"\)[/tex] on the drawing.
2. Convert Mixed Numbers to Decimals:
- [tex]\(3 \frac{1}{2}"\)[/tex] can be converted to a decimal by recognizing that [tex]\( \frac{1}{2} = 0.5 \)[/tex]. Thus, [tex]\(3 \frac{1}{2}" = 3.5" \)[/tex].
- [tex]\(5 \frac{1}{4}"\)[/tex] can be converted to a decimal by recognizing that [tex]\( \frac{1}{4} = 0.25 \)[/tex]. Thus, [tex]\(5 \frac{1}{4}" = 5.25" \)[/tex].
3. Calculate the Actual Dimensions Using the Scale:
Each inch on the drawing corresponds to 4 feet in reality.
- For the length:
[tex]\[
3.5 \text{ inches} \times 4 = 14 \text{ feet}
\][/tex]
- For the width:
[tex]\[
5.25 \text{ inches} \times 4 = 21 \text{ feet}
\][/tex]
4. Determine the Actual Size of the Bedroom:
The actual dimensions of the bedroom are 14 feet by 21 feet.
Therefore, the correct choice from the given options is:
C. [tex]\( 14 \, \text{ft} \times 21 \, \text{ft} \)[/tex]
