Pythagoras Experiment

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Recommended: Pythagoras and the Pythagorean theorem

Pythagoras Experiment

Aim: To investigate the relationships between the lengths of the 3

sides of the right angled triangles and the perimeters and areas of

these triangles.

Task 1:

a)

The numbers 5, 12, 13 satisfy the condition.

5² + 12² = 13²

Because 5² = 5x5 = 25

12² = 12x12 = 144

13² = 13x13 = 169

And so

5² + 12² = 25 + 144 = 169 = 132

b)

The Numbers 7, 24, 25 also satisfy the condition.

7² + 24² =25²

Because 7² = 7x7 = 49

24² = 24x24 = 576

25² = 25x25 = 525

And so

7² + 24² = 49+ 576 = 625 = 25²

Task2: The perimeter and area of the triangle are:

Perimeter = 5 + 12 + 13 = 30 units

Area = ½ x 5 x 12

= ½ x 60

= 30 square units

a)

5

12

13

[IMAGE]

b)

24

7

25

[IMAGE]

Perimeter = 7 + 24 + 25 = 56 units

Area = ½ x 7 x 24

= ½ x 168

= 84 square units

[IMAGE]

Length of shortest side

Length of middle side

Length of longest side

Perimeter

Area

3

4

5

12

6

5

12

13

30

30

7

24

25

84

84

Task3:

Length of short side is going to be in fixed steps meaning that this

is a linear sequence and the length of middle side and longest side is

actually a quadratic sequence because they are not in fixed steps and

in geometric sequence.

4 , 12 , 24 , 40

[IMAGE]

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