GCSE(F),

A drawing, map or model does not normally show the actual size of the object (or area, in the case of a map). The drawing shows the item **reduced** down (made smaller) or **enlarged** (made larger). 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.

1. A map shows details where 2km represents 5cm. What is the scale of this map?

Answer: 1: 40 000

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

2. 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?

Answer: 5..25m

The multiplier is 3.5 รท 1 = 3.5.

Multiply 3.5 x 150 = 525cm, or 5.25m.

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