Lesson Notes By Weeks and Term - Junior Secondary School 3







WEEK TEN                                          DATE---------------


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.


    Scale = Any length on scale drawing

                  Corresponding length on actual object


Worked Examples

  1. 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?


    1cm represents 2m

    5cm represents 5 × 2m = 10m

    The actual length of the billboard = 10m.

  1. An airport runway measuring 6000m is drawn to a scale of 1cm represents 500m. Find its 

    length on the drawing.


    500m is represented by 1cm

    1m is represented by 1/500cm

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

    Length on drawing = 12cm



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

Actual length


Length on drawing


1cm to 5m



1cm to 100m



1cm to 5m



  1.   Copy and complete the table by finding the actual length.

Length on drawing


Actual length


1cm to 5m



1cm to 100m



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

  1. 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.


Firstly, make a rough sketch of the plan



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


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.


                           178m                     124m 

                     A         108m             B          

Using a protractor, AXB = 370 (to the nearest degree). The angle between the paths is 370.



  1. Find the distance between the opposite corners of a rectangular room which is 12m by 9m. Use a scale of 1cm to 3m.
  2. 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

  1. The scale on a map is 1 : 50,000.
    1. Two villages A and B on the map are 5.5cm apart, find the actual distance in km between A and B.
    2. If town C is 4km from the village A, what is the distance of C from A on the map?


Note: Map scale = actual distance/distance on the map.

Distance on map = Actual distance / Map Scale

  1. 1cm represents 50,000cm

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

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

  1. 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?


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.


Evaluation: Class Work

  1. The scale on the map is 1 : 25,000.
  2. a) Find the distance in km between two islands represented by a distance of 20cm on the map.
  3. b) Find the distance between two towns on the map that are 10km apart..
  4. The scale of a map is 1 : 20,000. Find the actual distance in km represented by the map   

       by    a) 5cm          b) 10cm



NGM Bk 2 Chapter 16, Pages 133 – 134.

Essential Mathematics for JSS Bk 2, Chapter 17, Pg 166 – 169



  1. A quadrilateral has angles of 1280, 910, a0 and 2a0. Find the value of a0.
  2. a) 670 b) 470    c) 570    d) 1070
  3. The sum of the angles of a polygon is 16200, calculate the number of sides that the  

       polygon has.  a) 11    b) 21    c) 16    d) 13

  1. In fig. 1, PQRT and TQRS are parallelogram

    QR = 3cm and TQ = 4cm, what is PS?

  1. Which of the following are Pythagoras triple?  I (3, 4, 5) II (5, 12, 13)    III (8, 13, 17).
  2. a) III only b) I and II only        c) II only      d) II and III only.
  3. The diagonals of a rhombus measures 8cm y 6cm, what is the length of a side of the 

rhombus?    a) 8cm     b) 7cm     c) 10cm     d) 5cm



1.The scale on the map is 2cm : 30,000km

Find the distance in km between two islands represented by a distance of 20cm on the 

  1. A map of Nigeria shows scale of 1cm representing 75km. how far is it from Ibadan to kano, if the route distance measures 30.5cm on the map

© Lesson Notes All Rights Reserved 2023