To determine the actual dimensions of the bedroom using the given scale and drawing dimensions, we need to follow a few steps. Let's break it down:
1. Understanding the Scale:
The scale provided is [tex]\( \frac{1}{4} \, \text{inch} = 1 \, \text{ft} \)[/tex]. This means for every [tex]\(\frac{1}{4}\)[/tex] inch on the drawing, it represents 1 foot in real life.
2. Dimensions on Drawing:
- Length: [tex]\(6 \frac{3}{4} \, \text{inches}\)[/tex]
- Width: [tex]\(4 \frac{1}{2} \, \text{inches}\)[/tex]
Let's convert these mixed numbers to improper fractions to make calculations easier.
- Length: [tex]\(6 \frac{3}{4} \, \text{inches} = 6 \times 4 + 3 = 27 / 4 \, \text{inches}\)[/tex]
- Width: [tex]\(4 \frac{1}{2} \, \text{inches} = 4 \times 2 + 1 = 9 / 2 \, \text{inches}\)[/tex]
3. Calculate Actual Dimensions:
To find the actual size of the bedroom, we divide the drawing measurements by the scale factor [tex]\( \frac{1}{4}\)[/tex] inch per foot.
- For the length:
[tex]\[
\text{Actual Length} = \frac{27/4 \, \text{inches}}{\frac{1}{4} \, \text{inches/ft}} = \left(\frac{27}{4} \times \frac{4}{1}\right) \text{ft} = 27 \, \text{ft}
\][/tex]
- For the width:
[tex]\[
\text{Actual Width} = \frac{9/2 \, \text{inches}}{\frac{1}{4} \, \text{inches/ft}} = \left(\frac{9}{2} \times \frac{4}{1}\right) \text{ft} = 18 \, \text{ft}
\][/tex]
4. Answer Interpretation:
The actual dimensions of the bedroom are [tex]\(27 \text{ feet}\)[/tex] by [tex]\(18 \text{ feet}\)[/tex].
Therefore, the correct answer is:
C. [tex]\(18 \text{ ft}\)[/tex] by [tex]\(27 \text{ ft}\)[/tex]
