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Year 8 Interactive Maths - Second Edition


Scale Drawings

A map cannot be of the same size as the area it represents.  So, the measurements are scaled down to make the map of a size that can be conveniently used by users such as motorists, cyclists and bushwalkers.  A scale drawing of a building (or bridge) has the same shape as the real building (or bridge) that it represents but a different size.  Builders use scaled drawings to make buildings and bridges.

A ratio is used in scale drawings of maps and buildings.  That is:

Likewise, we have:


A scale is usually expressed in one of two ways:

  • using units as in 1 cm to 1 km
  • without explicitly mentioning units as in 1 : 100 000.

Note:

A scale of 1 : 100 000 means that the real distance is 100 000 times the length of 1 unit on the map or drawing.


Example 14

Write the scale 1 cm to 1 m in ratio form.

Solution:


Example 15

Simplify the scale 5 mm : 1 m.

Solution:


Example 16

Simplify the scale 5 cm : 2 km.

Solution:


Calculating the Actual Distance using the Scale

If the scale is 1 : x, then multiply the map distance by x to calculate the actual distance.


Example 17

A particular map shows a scale of 1 : 5000.  What is the actual distance if the map distance is 8 cm?

Solution:


Map distance = 8 cm

Let the actual distance be a cm.


Alternative Way:

Map distance = 8 cm


Calculating the Scaled Distance using the Actual Distance

If the scale is 1 : x, then divide the actual distance by x to calculate the map distance.


Example 18

A particular map shows a scale of 1 cm : 5 km.  What would the map distance (in cm) be if the actual distance is 14 km?

Solution:

So, the map distance is 2.8 cm.


Alternative Way:

So, the map distance is 2.8 cm.


Key Terms

scale drawing, map, scaled down, scale of a drawing, map scale


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