Answer:
[tex]Model = 80cm[/tex]
Step-by-step explanation:
Given
[tex]Length = 19.2\ m[/tex]
[tex]Scale=1:24[/tex]
Required
Determine the scale measurement in centimeters
The scale can be represented as: [tex]Model : Actual[/tex]
[tex]Scale = Model : Actual[/tex]
Substitute 19.2 for Actual Length
[tex]Scale = Model : 19.2\ m[/tex]
Represent as a fraction
[tex]Scale = \frac{Model}{19.2m}[/tex] --- (1)
Recall that:
[tex]Scale=1:24[/tex]
Represent as a fraction
[tex]Scale = \frac{1}{24}[/tex] --- (2)
Equate (1) & (2)
[tex]\frac{Model}{19.2m} = \frac{1}{24}[/tex]
Multiply through by 19.2m
[tex]Model = \frac{1}{24} * 19.2m[/tex]
[tex]Model = \frac{ 19.2m}{24}[/tex]
Convert to centimeter
[tex]Model = \frac{ 19.2 * 100cm}{24}[/tex]
[tex]Model = \frac{ 1920cm}{24}[/tex]
[tex]Model = 80cm[/tex]
Hence, the length of the scale model is 80 cm
