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The scale model of a rectangular garden is [tex]1.5 \, \text{ft}[/tex] by [tex]4 \, \text{ft}[/tex]. The scale model is enlarged by a scale factor of 7 to create the actual garden. What is the area of the actual garden?

A. [tex]6 \, \text{ft}^2[/tex]
B. [tex]42 \, \text{ft}^2[/tex]
C. [tex]252 \, \text{ft}^2[/tex]
D. [tex]294 \, \text{ft}^2[/tex]

Sagot :

GinnyAnswer
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].
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