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Zorluk: KolayScale Drawings

A state map uses a scale where 1 inch1\text{ inch} represents 50 miles50\text{ miles}. If the straight-line distance between two cities on the map is 2.5 inches2.5\text{ inches}, what is the actual distance between the two cities?

  1. A
    20 miles20\text{ miles}
  2. B
    12.5 miles12.5\text{ miles}
  3. 125 miles125\text{ miles}Cevap
  4. D
    2.5 miles2.5\text{ miles}

Cevap

125 miles125\text{ miles}
The map scale indicates that every 1 inch on the map corresponds to 50 actual miles. To find the real-world distance for a measurement of 2.5 inches on the map, you must multiply the map measurement by the scale factor: 2.5 × 50 = 125 miles.

Adım Adım Çözüm

1
Set up a proportion or identify the scale factor from the problem description.
1 inch=50 miles1\text{ inch} = 50\text{ miles}
This establishes how many real-world miles are represented by each inch on the map.
2
Multiply the measured map distance by the scale factor to find the actual distance.
2.5 inches×50 miles/inch=125 miles2.5\text{ inches} \times 50\text{ miles/inch} = 125\text{ miles}
Since every inch represents 50 miles, 2.5 inches will represent 2.5 groups of 50 miles.

Anahtar Kavram

Using a linear scale factor to convert a map measurement to a real-world distance.
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