Ratio, SM-Bank 043

The scale on a map is \(4:20\ 000\).

For each of these scaled distances, find the actual distances in kilometres.

\(2\ \text{cm}\) (1 mark)

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\(5\ \text{mm}\) (1 mark)

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\(18.4\ \text{cm}\) (1 mark)

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Show Answers Only

a. \(100\ \text{m or } 0.1\ \text{km}\)

b. \(40\ \text{m or } 0.04\ \text{km}\)

c. \(920\ \text{m or } 0.92\ \text{km}\)

Show Worked Solution

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

a.	\(\text{Actual Distance}\)	\(=2\ \text{cm}\times 5000 \)
		\(= 10\ 000\ \text{cm}\)
		\(=100\ \text{m}=0.1\ \text{km}\)

b.	\(\text{Actual Distance}\)	\(=8\ \text{mm}\times 5000 \)
		\(=40\ 000\ \text{mm}\)
		\(=40\ \text{m}=0.04\ \text{km}\)

c.	\(\text{Actual Distance}\)	\(=18.4\ \text{cm}\times 5000 \)
		\(= 92\ 000\ \text{cm}\)
		\(=920\ \text{m}=0.92\ \text{km}\)