Answer :
To solve this problem, we need to convert the measured distances on paper to real-world distances using the given scale of 1:250,000. This scale means that 1 cm on the map or paper represents 250,000 cm in real life. To convert from cm on the map to km in real life, we'll follow these steps:
- Convert from cm to real-world cm: Multiply the measured distance by the scale factor (250,000).
- Convert cm to km: Since 1 km = 100,000 cm, divide the real-world distance in cm by 100,000.
Let's apply this to each of the measured distances:
45 cm on paper:
[tex]\text{Real-world distance in cm} = 45 \times 250,000 = 11,250,000 \text{ cm}[/tex]
[tex]\text{Convert to km} = \frac{11,250,000}{100,000} = 112.5 \text{ km}[/tex]10 cm on paper:
[tex]\text{Real-world distance in cm} = 10 \times 250,000 = 2,500,000 \text{ cm}[/tex]
[tex]\text{Convert to km} = \frac{2,500,000}{100,000} = 25 \text{ km}[/tex]105 mm on paper:
First, convert mm to cm. We know 10 mm = 1 cm, so:
[tex]105 \text{ mm} = 10.5 \text{ cm}[/tex]
[tex]\text{Real-world distance in cm} = 10.5 \times 250,000 = 2,625,000 \text{ cm}[/tex]
[tex]\text{Convert to km} = \frac{2,625,000}{100,000} = 26.25 \text{ km}[/tex]250 mm on paper:
Convert mm to cm:
[tex]250 \text{ mm} = 25 \text{ cm}[/tex]
[tex]\text{Real-world distance in cm} = 25 \times 250,000 = 6,250,000 \text{ cm}[/tex]
[tex]\text{Convert to km} = \frac{6,250,000}{100,000} = 62.5 \text{ km}[/tex]
These steps help us understand how distances on a map scale translate to real-world distances. Always ensure unit conversions are handled carefully, especially between mm and cm, as well as when switching from cm to km.
