the scale on a map is 1:500,000. Two towns are 7 cm apart on the map. Work out the actual distance between the towns
Answers
Scales are used on maps in the same way that they are used in plans.
A scale of 1 : 50 000 is used on many Ordnance Survey maps.
This means that 1 cm on the map represents an actual distance of 50 000 cm (or 500 m or 0.5 km).
Converting measurements on a map
We saw above that if a map has a scale of 1 : 50000, then 1 cm on the map is 50000 cm in real life.
(a) Imagine we have measured a distance as 3 cm on this map, and we want to find out how far this is in real life.
To work out the distance in real life, we need to multiply this length by 50000.
This gives 3 cm × 50000 = 150000 cm which is 1500 m or 1.5 km.
Alternatively, we could have just remembered that each 1 cm on the map is 0.5 km in real life.
Hence, 3 cm on the map must be 3 × 0.5 km = 1.5 km in real life.
(b) Now imagine we want to walk 4.5 km in real life, and we need to find out how far this is on the map.
To work out the distance on the map, we need to divide this length by 50000.
4.5 km = 4500 m = 450000 cm. Dividing 450000 cm by 50000 gives a distance on the map of 9 cm.
Alternatively, we could have just remembered that each 0.5 km in real life is 1 cm on the map.
If we divide 4.5 km by 0.5 km we get 9, so the distance on the map must be 9 cm.