SCALE

A scale is used to reduce the actual distance between two points on a map . The scale of a map is an example of ratio. The ratio is often in the form 1: n.
For example, 1: 50000 means 1 cm on the map represents 50000 cm on the ground. You can see the scale of a map, drawing or model to calculate lengths.
If you know the real length, you can find the matching 'scale length' or the length on the map.
Also, if you know the 'scale length' or the length on the map, you can find the real length.
If the scale of map is 1: n, then;
1. The distance on the ground or real length = n × distance on the map.
2. The distance on the map = distance on the ground or real length/n
Note that you can find the scale if you know the length on the map and the actual length.
3. Scale = lenght on the map: actual length. You have to put your answer in the form
 1: n.
NOTE: that to give the scale in a ratio, the two lengths must be in the same unit. Change one of them if you need to.

EXAMPLE

A map is drawn to a scale of 1: 20000.
a) Find the distance on the map between two points that are 12 km apart.
b) The distance on the map between two villages is 25 cm. Find the real distance between the two villages.

SOLUTION

1: 20000 means 1 cm on the map represents 20000 cm but 1 km = 100000cm.
Hence 1 cm represents 0.2 km or 5 cm represents 1 km
a) 12 km is represented by 12 × 5 cm = 60 cm
b) 25cm represents 25× 0.2 km = 5 km

ASSIGNMENT

A map is drawn to a scale of 1: 40000. Find
i) the distance on the map between two places that are 20 km apart.
ii) the actual distance between two places that are 18.5 cm apart on the map.