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Ratio, SM-Bank 044

A model train is built using a scale of \(4:20\ 000\).

For each of these actual lengths, find the scaled length.

  1. \(40\ \text{m}\)  (1 mark)

  2. \(87\ 450\ \text{cm}\)  (1 mark)

  3. \(2400\ \text{m}\)  (1 mark)

Show Answers Only

a.    \(\text{8 mm or 0.8 cm}\)

b.    \(\text{17.49 cm or 0.1749 m}\)

c.    \(\text{48 cm or 0.48 m}\)

Show Worked Solution

\(\text{Scale}\ \rightarrow\ 4:20\ 000=1:5000\)

a.    \(\text{Scaled length }\) \(\dfrac{40}{5000}\ \text{m}=\dfrac{40\ 000}{5000}\ \text{mm}\)
    \(=\text{8 mm}=\text{0.8 cm}\)

 

b.    \(\text{Scaled length}\) \(=\dfrac{87\ 450}{5000}\ \text{cm} \)
    \(=\text{17.49 cm}=\text{0.1749 m}\)

 

c.    \(\text{Scaled length}\) \(=\dfrac{2400}{5000}\ \text{m}=\dfrac{240\ 000}{5000}\ \text{cm}\)
    \(=\text{48 cm}=\text{0.48 m}\)