Back to: MATHEMATICS JSS3

**Welcome to Class !!**

*We are eager to have you join us !!*

*In today’s Mathematics class, We will be talking about Scale Drawing. We hope you enjoy the class!*

**Using Scales**

A scale is a ratio or proportion that shows the relationship between a length or a drawing and the corresponding length on the actual object.

Thus,

$\mathit{S}\mathit{c}\mathit{a}\mathit{l}\mathit{e}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{A}\mathbf{n}\mathbf{y}\mathbf{}\mathbf{l}\mathbf{e}\mathbf{n}\mathbf{g}\mathbf{t}\mathbf{h}\mathbf{}\mathbf{o}\mathbf{n}\mathbf{}\mathbf{s}\mathbf{c}\mathbf{a}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{d}\mathbf{r}\mathbf{a}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{g}}{\mathbf{C}\mathbf{o}\mathbf{r}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{p}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{}\mathbf{l}\mathbf{e}\mathbf{n}\mathbf{g}\mathbf{t}\mathbf{h}\mathbf{}\mathbf{o}\mathbf{n}\mathbf{}\mathbf{a}\mathbf{c}\mathbf{t}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{o}\mathbf{b}\mathbf{j}\mathbf{e}\mathbf{c}\mathbf{t}}$

**Worked Examples**

- The scale drawing of the length of an advertisement billboard measures 5cm. What is the actual length of the billboard if the scale is 1cm represents 2m?

**Solution**

1cm represents 2m

5cm represents 5 × 2m = 10m

The actual length of the billboard = 10m.

- An airport runway measuring 6000m is drawn to a scale of 1cm represents 500m. Find its length on the drawing.

** Solution**

500m is represented by 1cm

1m is represented by 1/500cm

6000m is represented by 6000 × 1/500 = 12cm

Length on drawing = 12cm

** **

**Evaluation: **

1) Copy and complete the table below in finding the length on drawing giving a suitable scale.

Actual length |
Scale |
Length on drawing |

20m | 1cm to 5m | |

450m | 1cm to 100m | |

65m | 1cm to 5m |

2) Copy and complete the table by finding the actual length.

Length on drawing |
Scale |
Actual length |

11cm | 1cm to 5m | |

8.2cm | 1cm to 100m | |

12.6cm | 2cm to 1m |

**Scale Drawing**

Scale drawing is very important to engineers, architects, surveyors and navigators. For an accurate scale drawing, mathematical instruments are needed such as pencils, a ruler and a set-square. Also, the dimensions of the actual objects are written on the drawing.

** **

**Worked Examples**

- A rectangular field measures 45m by 30m. Draw a plan of the field. Use measurement to find the distance between opposite corners of the field.

**Solution**

Firstly, make a rough sketch of the plan

45m

30m

Secondly, choose a suitable scale

Using 1cm represent5m will give a 9cm by 6cm rectangle.

The distance between the opposite corners of the field is represented by the dotted line. Length of the dotted line = 10.75

Actual distance = 10.75 × 5 = 53.75m = 54m (to the nearest metre)

**Example 2: **

Points A and B are 178m and 124m from X respectively. The distance between A and B is 108m. Make a scale drawing of the path and find the angle between the paths and X. X

**Solution**

178m 124m

A B

108m

Using a suitable scale of 1cm to 20m, the sides of the triangle in scale drawing will be as follows:

AX = 178/20 = 8.9cm, BX = 124/20 = 6.2cm, AB = 108/20 = 5.4cm.

X

178m 124m

A 108m B

Using a protractor, AXB = 37^{0} (to the nearest degree). The angle between the paths is 37^{0}.

** **

**Evaluation: **

- Find the distance between the opposite corners of a rectangular room which is 12m by 9m. Use a scale of 1cm to 3m.
- A triangular plot ABC is such that AB = 120m, BC = 80m and CA = 60m. P is the middle point of AB. Find the length of PC. Use a scale of 1cm to 10m.

** **

**Application of Scale Drawing on Related Problems**

Worked Examples

- The scale on a map is 1: 50,000.

a) Two villages A and B on the map are 5.5cm apart, find the actual distance in km between A and B.

b) If town C is 4km from the village A, what is the distance of C from A on the map?

**Solution**

$Note:MapScale=\frac{Actualdis\mathrm{tan}ce}{dis\mathrm{tan}ceonthemap}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\therefore Dis\mathrm{tan}ceonmap=\frac{Actualdis\mathrm{tan}ce}{Mapscale}$

a) 1cm represents 50,000cm

5.5cm represent 50,000 × 5.5 = 275,000cm

To correct to km = 275,000/100,000 = 2.75km.

b) 1km = 100,000cm

4km = 100,000 × 4 = 400,000cm.

Since 50,000cm represents 1cm

400,000cm is represented by 400,000/50,000 = 8cm

or Distance on the map = Actual distance / Map Scale

= 400,000 / 50,000 = 8cm.

**Example 2:**

Two cities are 70km apart. The distance between them is 20cm on the map. What is the scale of the map?

**Solution**

1km = 100,000cm

∴ 70km = 100,000 × 70 = 7,000,000cm

Map scale = actual distance/distance on map.

= 7,000,000/20 = 350,000

The scale of the map = 1: 350,000.

*We have come to the end of this class. We do hope you enjoyed the class?*

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