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A parking lot is going to be [tex]50 \, \text{m}[/tex] wide and [tex]150 \, \text{m}[/tex] long. Which dimensions could be used for a scale model of the lot?

A. [tex]10 \, \text{m} \times 25 \, \text{m}[/tex]
B. [tex]75 \, \text{in} \times 225 \, \text{cm}[/tex]
C. [tex]100 \, \text{cm} \times 300 \, \text{m}[/tex]
D. [tex]25 \, \text{cm} \times 75 \, \text{cm}[/tex]

Sagot :

GinnyAnswer
To determine which dimensions could be used for a scale model of the parking lot that is 50 meters wide and 150 meters long, we need to consider the given choices and establish whether any of these can accurately represent a scaled-down version of the lot.

### Step-by-Step Solution:

1. Understanding the Actual Dimensions:
- Width (actual): [tex]\( 50 \)[/tex] meters
- Length (actual): [tex]\( 150 \)[/tex] meters

2. Convert All Choices to the Same Unit (meters):
- Option A: [tex]\( 10 \)[/tex] meters [tex]\( \times 25 \)[/tex] meters
- No conversion needed.
- Option B: [tex]\( 75 \)[/tex] inches [tex]\( \times 225 \)[/tex] centimeters
- 1 inch = 0.0254 meters
- 75 inches = [tex]\( 75 \times 0.0254 = 1.905 \)[/tex] meters
- 1 centimeter = 0.01 meters
- 225 centimeters = [tex]\( 225 \times 0.01 = 2.25 \)[/tex] meters
- Converted dimensions: [tex]\( 1.905 \)[/tex] meters [tex]\( \times 2.25 \)[/tex] meters
- Option C: [tex]\( 100 \)[/tex] centimeters [tex]\( \times 300 \)[/tex] meters
- 100 centimeters = [tex]\( 100 \times 0.01 = 1 \)[/tex] meter
- No conversion needed for the length.
- Converted dimensions: [tex]\( 1 \)[/tex] meter [tex]\( \times 300 \)[/tex] meters
- Option D: [tex]\( 25 \)[/tex] centimeters [tex]\( \times 75 \)[/tex] centimeters
- 25 centimeters = [tex]\( 25 \times 0.01 = 0.25 \)[/tex] meters
- 75 centimeters = [tex]\( 75 \times 0.01 = 0.75 \)[/tex] meters
- Converted dimensions: [tex]\( 0.25 \)[/tex] meters [tex]\( \times 0.75 \)[/tex] meters

3. Analyze each Option:
For a model to be a scale model, both the width and length should be scaled by the same factor.

- Option A:
- Width ratio: [tex]\( \frac{50}{10} = 5 \)[/tex]
- Length ratio: [tex]\( \frac{150}{25} = 6 \)[/tex]
- Ratios do not match. This option is not valid.

- Option B:
- Width ratio: [tex]\( \frac{50}{1.905} \approx 26.24 \)[/tex]
- Length ratio: [tex]\( \frac{150}{2.25} \approx 66.67 \)[/tex]
- Ratios do not match. This option is not valid.

- Option C:
- Width ratio: [tex]\( \frac{50}{1} = 50 \)[/tex]
- Length ratio: [tex]\( \frac{150}{300} = 0.5 \)[/tex]
- Ratios do not match. This option is not valid.

- Option D:
- Width ratio: [tex]\( \frac{50}{0.25} = 200 \)[/tex]
- Length ratio: [tex]\( \frac{150}{0.75} = 200 \)[/tex]
- Ratios do match. This option is valid.

### Conclusion:
Upon analyzing all the options, we find that none of the dimensions except for Option D correctly create a scale model of the parking lot, thereby reflecting accurate scaled-down ratios.

Therefore, the valid dimensions for the scale model are:

None of the choices given are valid for making a scale model.
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