Unspecified Scale
Being able to convert between the different measures of metric length is often an essential skill when attempting to solve many of the problems concerning scale – especially unspecified scale. For help on this see: Converting between metric measures of length.
The importance of being able to convert between measures of length
The measurements taken from scale plans, maps, models or drawings are multiplied up to find the actual length of the distance being represented. Hence, if a measurement of 5cm is made on a map with a scale of 1:10 000, then the actual distance is 5cm X 10 000 = 50 000cm. However, the magnitude of this distance is too great to be expressed in centimetres, and would be converted to metres: 50 000 cm ÷ 100 = 500m. Therefore it is important to be able to convert between the various metric measures when solving problems concerning scale.
Solving problems concerning unspecified scale
A drawing of a new council building has a scale of 1:250 This scale does not specify a unit of measurement to use – so any measure taken is scaled by 250 using the same units of measure and converted afterwards.
1) A wall on the drawing measures 20cm, what is the length of the actual wall in metres?
In order to solve this problem the measurement taken from the drawing needs to first of all be multiplied by 250 – because everything on the actual building is 250 times larger than on the drawing. 20cm X 250 = 5 000cm. However, the question asked the actual distance to be given in metres. 5 000cm converts to 50m.
2) The main meeting room in the new building is 15m long. How many centimetres long is the corresponding room on the drawing?
In this question the actual, real-life distance has been given and the corresponding distance has to be found on the drawing. In order to solve this problem, the actual distance has to be reduced, or ‘shrunk’, down by 250 times – this is done by dividing it by 250. Before doing this though it is best to convert the actual distance into the units required by the question. So 15m = 1500cm. Now the 1500cm needs to be made 250 times smaller: 1500cm/250 = 150cm/25 = 6cm. So the room on the drawing is 6cm long.
To prove the answer we can work the other way:
6cm on the drawing X 250 = 1 500cm on the actual building. 1 500cm = 15m.
Note that it is also important to realise the difference between being given the actual measurements and the measurements on the map, plan, model or drawing. This is the first thing to decide when dealing with unspecified scale questions – maps, plans, models and drawings are usually represented by the 1 side of a scale (otherwise theplan etc would be bigger than the real thing). So in a scale of 1:50 the actual, real-life measurement is 50 times larger than on the plan etc.