A drawing, map or model does not normally show the actual size of an object or area. The drawing shows the item reduced or enlarged in size. The amount by which the size is changed is known as the scale factor, and is shown as a ratio.
A scale of 1:100 means that the drawing is 1/100th of the size of the real thing. On a map, a scale of 1:10 000 means that every centimetre on the map is 10 000cm, or 100m, on the ground.
A map shows details where 2km represents 5cm. What is the scale of this map?
Change km to cm so that all measurements are in the same units:
2 x 1000 x 100 (convert km to cm) = 200 000cm.
The scale is 5 : 200 000,
Simplify both sides by dividing by 5
1: 40 000
Answer: 1: 40 000
On a drawing, the length of a house is shown as 3.5cm. The scale of the drawing is 1: 150. What is the actual length of the house?
The multiplier is 3.5 ÷ 1 = 3.5.
Multiply 3.5 x 150 = 525cm, or 5.25m.