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A parking lot is going to be 40 m wide and 100 m long. Which dimensions could be used for a scale model of the lot?

A. [tex]25 \, \text{cm} \times 75 \, \text{cm}[/tex]

B. [tex]10 \, \text{cm} \times 25 \, \text{cm}[/tex]

C. [tex]100 \, \text{cm} \times 300 \, \text{m}[/tex]

D. [tex]75 \, \text{in} \times 225 \, \text{cm}[/tex]



Answer :

GinnyAnswer
To determine which dimensions can be used for a scale model of a parking lot that is 40 meters wide and 100 meters long, we need to compare the aspect ratios of the proposed scale models with the actual lot. The aspect ratio is the ratio of the width to the length.

Step 1: Calculate the aspect ratio of the actual parking lot.
- Width = 40 meters
- Length = 100 meters
- Aspect ratio = Width / Length = 40 / 100 = 0.4

Step 2: Calculate the aspect ratios for each of the given scale model options.

Option A: 25 cm × 75 cm
- Width = 25 cm
- Length = 75 cm
- Aspect ratio = 25 / 75 = 0.3333333333333333

Option B: 10 cm × 25 cm
- Width = 10 cm
- Length = 25 cm
- Aspect ratio = 10 / 25 = 0.4

Option C: 100 cm × 300 m
- Width = 100 cm
- Length = 300 meters (note: 1 meter = 100 cm, so 300 m = 30000 cm)
- Aspect ratio = 100 / 30000 = 0.0033333333333333335

Option D: 75 in × 225 cm
- Width = 75 inches (note: 1 inch = 2.54 cm, so 75 in = 75 * 2.54 = 190.5 cm)
- Length = 225 cm
- Aspect ratio = 190.5 / 225 = 0.8466666666666667

Step 3: Compare the aspect ratios of the scale model options with the aspect ratio of the actual parking lot (0.4).

- Option A: 0.3333333333333333
- Option B: 0.4
- Option C: 0.0033333333333333335
- Option D: 0.8466666666666667

Conclusion:
The scale model that has the same aspect ratio as the actual parking lot (0.4) and therefore can be used to create a scale model of the parking lot is:

Option B: 10 cm × 25 cm

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