Practical uses of scale factors
A scale factor can be used to create maps and other scale diagrams.
When things are too big to draw on paper, scale factors are used to calculate smaller, proportional measurements.
Floor plans for house designs are drawn on a smaller scale. This will help a designer to see if things will fit together well in each room of the house.
Scales in maps and diagrams are usually shown as a ratio.
The scale used on this plan (1:100) means that every 1 cm on the page is 1 m in real life.
Converting using a scale factor
To convert from a scale drawing to real life, measure a line in the drawing and multiply it by the scale factor to find the real length.
Question
If a floor plan shows a scale of \(1 \:\text{cm} : 100 \:\text{cm}\) and the kitchen measures 4 cm long on the drawing, how long is the kitchen in real life?
The real kitchen size would be \(4 \times 100 = 400 \:\text{cm}\) (or 4 m) long.
To convert from real life to a scale drawing, divide the real life measurement by the scale factor.
Question
If a map is drawn using a scale factor where 2 cm represents 3.5 km and the distance between Brora and Golspie is 8.5 km then what would the length of the drawing showing the same distance be?
The length on the drawing would be \(2 \div 3.5 \times 8.5 = 4.9 \:\text{cm}\) (to 1 dp).