Pythagoras

Pythagoras was a Greek mathematicianwho was born approximately 2700 years ago. He was responsible for figuring out a lot of modern maths,especially geometry and trigonometry.

History

Pythagoras is said to have come up with a rule to work out the sides of a right angled triangle.

Pythagoras’ Rule The rule only works for right angled triangles.

The rule says that if you square (times by themselves) the two short sides of a triangle then add them together it will equal the square of the long side.

Short Long 1

Short 2

c a

b

a2 + b2 = c2

c a

b

short2 + short2 = long2

1. Square both short sides2. Add the squares together3. Square-root your answer

To find the long side

3 x

4

32 + 42 = x2

9 + 16 = 25a = √25 = 5

short2 + short2 = long2

rearrange

short2 = long2 - short2

1. Square the sides2. Subtract the short square from the long

square3. Square-root your answer

To find a short side

a 20

16202 – 162 = a2

400 - 256 = 144a = √144 = 12

Practice Questions

1.

6

8

x

Practice Questions

2.

4

7

x

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3.

0.3

0.6

x

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4.

28

19

x

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5.

6

8x

Practice Questions

6.

100

130

x

Practice Questions

7.

1118

x

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8.

7.4

5.5

x

Practice Questions

9.

8 3

x

Practice Questions

10.

90

55x