# Linear Measurement or Length

**Class****:- Basic 6**

**Subject****:- Mathematics**

**Week****:- 3**

**Topic****: ****Length **

**Behavioral objective:-**

** At the end of the lesson the pupils should be able to:-**

** 1. Recognize and convert the units of Length measurements from one units to another **

**Apply Pythagoras’ rule or theorem to find the unknown length of a given right-angled triangle****Identify Pythagorean triplets****4. Find the heights and distances of objects**

**Instructional material/Reference material:-**

** Online Materials **

**Textbooks **

**Scheme of Work By Lagos state **

**Pictures of Triangles **

**Building Background /connection to prior knowledge :**** **

**Students are familiar with the various ways of measuring length in their previous lessons **

**Conten****t:- **

**LENGTH**

**The standard unit of length are:****– **

**10 millimetres (mm) make one **** centimetre**

10 centimetres (cm) make one decimetre

10 decimetres (dm) make one metre

100 centimetre make one metre

1000 metres make one kilometre

The measurements can also be written in inverse way in this way

**10 millimetres (mm) = 1 centimetre (cm)**

** 1000 millimetres = 1 metre**

**100 centimetres = 1 metre**

**10 Decimetres 1 Metre **

**1000 metres = 1 kilometre (km)**

**Examples****1. **

**10mm = 1cm**

**Therefore 18cm = 18 × 10mm = 180mm**

**1000m = 1km****1.08km = 1.08 × 1000m = 1080m**

**Examples**

**1} 10mm = 1cm**

**∴ 280mm = 280 ÷ 10cm**

** = 28cm**

**2} 100cm = 1m ****∴ 185cm = 185 ÷ 100m = 1.85m**

**Pythagoras theorem**

Study the diagrams below

**Triangles ABC, LMN and XYZ are right-angled triangles**

**.****Bˆ, Mˆ and Yˆ are right angles (i.e. 90º)**

** The side facing (opposite) each right angle is the longest side. **

**This side is called the hypotenuse.**

** That is, AC, LN and XZ are the hypotenuses of triangles ABC, LMN and XYZ respectively.**

**ABC is a right-angled triangle with Bˆ = 90º **

**AB = 3cm, BC = 4cm and AC = 5cm**

**Area of red square = 3cm × 3cm = 9cm**

**2 ****Area of blue square = 4cm × 4cm = 16cm2**** **

**Area of red square + Area of blue square 9cm2 + 16cm2 = 25cm2****Area of black square = 5cm × 5cm = 25cm2**

**From the calculation, you will see that the area of the black square equals the sum of the areas of both the red square and blue square.****This is called the Pythagoras theorem. In this right-angled triangle ABC, **

**pythagoras’ theorem tells you that area Y (black) = area R (red) + area B (blue)****Pythagoras’ theorem**

**In any right-angled triangle, the area of the square on the hypotenuse side is equal to the sum of the areas of the squares on the other two sides**

**Application of Pythagoras’ theorem to calculate the missing side of a right-angled triangle**

**Pythagoras’ theorem is usually written us****ing the lengths of the sides of the triangle.****In this right-angled triangle ABC, ****Pythagoras’ theorem tells you that**

**b2 = a2 + c2**

**The square of the hypotenuse side is **

**equal to the sum of the squares of the other two sides.****This rule is used to find an unknown side of a right-angled triangle when the other two sides are given.**

**Example****1. Study how the length of the side marked y is found.**

**Hypotenuse = 13cm****∴ 132 = y2 + 52**

**∴ 169 = y2 + 25**

**169 – 2****5 = y**

**2****√144 = y2**

**∴ y2 = 144****y **

**= 144 **

**= 12cm**

**E****valuation:-**

1. Convert 3000 cm to kilomètres

**Find the length of the hypotenuse of a right-angled triangle if the lengths of the other two sides are 12cm and 16cm respectively.****3. A right-angled triangle has its hypotenuse as 10cm and one other side as 8cm. Calculate the length of the third side**