To solve this problem, we will determine the actual dimensions of the shed by using the given model dimensions and applying the scale factor.
The model dimensions are:
- Length: [tex]\(1 \frac{3}{4}\)[/tex] feet
- Height: [tex]\(1 \frac{1}{2}\)[/tex] feet
- Width: [tex]\(1 \frac{1}{4}\)[/tex] feet
The scale factor is 6, which means the actual shed is six times larger than the model.
1. Length Calculation:
- Model length = [tex]\(1 \frac{3}{4}\)[/tex] feet
- Converting the mixed number to an improper fraction: [tex]\(1 \frac{3}{4} = \frac{7}{4}\)[/tex] feet
- Actual length = [tex]\(\frac{7}{4} \times 6 = \frac{42}{4} = 10.5\)[/tex] feet
2. Height Calculation:
- Model height = [tex]\(1 \frac{1}{2}\)[/tex] feet
- Converting the mixed number to an improper fraction: [tex]\(1 \frac{1}{2} = \frac{3}{2}\)[/tex] feet
- Actual height = [tex]\(\frac{3}{2} \times 6 = \frac{18}{2} = 9\)[/tex] feet
3. Width Calculation:
- Model width = [tex]\(1 \frac{1}{4}\)[/tex] feet
- Converting the mixed number to an improper fraction: [tex]\(1 \frac{1}{4} = \frac{5}{4}\)[/tex] feet
- Actual width = [tex]\(\frac{5}{4} \times 6 = \frac{30}{4} = 7.5\)[/tex] feet
Therefore, the dimensions of the actual shed are:
- Length: 10.5 feet
- Height: 9 feet
- Width: 7.5 feet
Among the given options, the correct dimensions that match our calculated results are:
[tex]\(10 \frac{1}{2}\)[/tex] feet by 9 feet by [tex]\(7 \frac{1}{2}\)[/tex] feet.
Thus, the correct option is:
[tex]\( \boxed{10 \frac{1}{2}} \text{ feet by 9 feet by } 7 \frac{1}{2} \text{ feet}\)[/tex]
