Alright, let's solve this step-by-step.
1. Understand the Problem:
- We have a scale model of a rectangular garden.
- The dimensions of this scale model are [tex]\(1.5\)[/tex] feet in length and [tex]\(4\)[/tex] feet in width.
- This model is enlarged by a scale factor of [tex]\(7\)[/tex] to create the actual garden.
- We need to determine the area of the actual garden.
2. Scale Factor Application:
- To find the dimensions of the actual garden, we multiply the dimensions of the scale model by the scale factor.
3. Calculate the Dimensions of the Actual Garden:
- Length: [tex]\(1.5 \text{ ft} \times 7 = 10.5 \text{ ft}\)[/tex]
- Width: [tex]\(4 \text{ ft} \times 7 = 28 \text{ ft}\)[/tex]
4. Calculate the Area of the Actual Garden:
- The area of a rectangle is given by the formula:
[tex]\[
\text{Area} = \text{Length} \times \text{Width}
\][/tex]
- Using the dimensions we've calculated:
[tex]\[
\text{Area} = 10.5 \text{ ft} \times 28 \text{ ft} = 294 \text{ ft}^2
\][/tex]
5. Result:
- The area of the actual garden is [tex]\(294 \text{ ft}^2\)[/tex].
So, the correct answer is [tex]\(294 \text{ ft}^2\)[/tex].
