1227 Words5 Pages

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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