Answer:
[tex]L =100cm[/tex]
Explanation:
Given
[tex]Scale = \frac{1}{2000}[/tex] ----- [tex]Length = 50cm[/tex]
Required
Determine the length when the scale is: [tex]Scale = \frac{1}{1000}[/tex]
The scale to length can be represented as:
[tex]Ratio = Scale: Length[/tex]
Represent as fraction
[tex]Ratio = \frac{Scale}{Length}[/tex]
When:
[tex]Scale = \frac{1}{2000}[/tex] and [tex]Length = 50cm[/tex]
[tex]Ratio = \frac{1/2000}{50cm}[/tex]
When [tex]Scale = \frac{1}{1000}[/tex], represent the length with L
[tex]Ratio = \frac{1/1000}{L}[/tex]
Equate both ratios
[tex]\frac{1/2000}{50cm} = \frac{1/1000}{L}[/tex]
Cross Multiply:
[tex]L * \frac{1}{2000} = 50cm * \frac{1}{1000}[/tex]
Multiply through by 2000
[tex]L * \frac{1}{2000} * 2000 = 50cm * \frac{1}{1000} * 2000[/tex]
[tex]L = 50cm * 2[/tex]
[tex]L =100cm[/tex]
Hence, the length on the new scale would be 100cm
