Map scales A scale drawing is a drawing in which all dimensions have been reduced in exactly the same proportion. For example, if a model boat is made to a scale of 1:20 (1 to 20), this scale can be applied to any units, so that 1mm measured on the model is 20mm on the actual boat, 1cm measured on the model is 20cm on the actual boat, and so on...

Worked example a) If the 1:20 model boat is 15cm wide, how wide is the actual boat? b) If the boat has a mast of height 4m, how high is the mast on the model? Solution: The scale is 1:20. This means that every cm on the model is equivalent to 20cm on the real boat.

Solution a) 1cm on the model = 20cm on the actual boat, so we calculate 15cm x 20 = 300cm. 15cm on the model = 300cm (3m) on the actual boat b) 20cm on the actual boat = 1cm on the model, so we calculate  400cm  = 20cm 20 400cm (4m) on the actual boat = 20cm on the model

Sample question Now try the following question: The scale of a map is 1:50 000 a) A distance is measured as 2cm on the map. i) How many cm is this equivalent to in real life? 1 cm on the map represents 50 000cm in real life. Therefore, 2cm on the map represents 100 000cm in real life.

Sample question ii) How many m is this equivalent to? To convert from cm to m, we divide by 100. 100000cm = 1000m iii) How many km is this equivalent to? To convert from m to km we divide by 1000. 1000m = 1km.

Sample question b) What distance on the map will represent 5km in real life?(Hint: Use your answers to part a) to help you!) In part a) we saw that 1km in real life was equivalent to 2cm on the map. Therefore, 5km in real life is equivalent to 10cm on the map.