Investigating the Relationship Between the Lengths, Perimeter and Area of a Right Angle Triangle
Coursework
Aim
To investigate the relationships between the lengths, perimeter and
area of a right angle triangle.
Pythagoras Theorem is a² + b² = c². 'a' being the shortest side, 'b'
being the middle side and 'c' being the longest side of a right angled
triangle.
So the (smallest number)² + (middle number)² = (largest number)²
The number 3, 4 and 5 satisfy this condition
3² + 4² = 5²
because 3² = 3 x 3 = 9
4² = 4 x 4 = 16
5² = 5 x 5 = 25
and so 3² + 4² = 9 + 16 = 25 = 5²
The numbers 5,12, 13 and 7,24,25 also work for this theorem
5² + 12² = 13²
because 5² = 5 x 5 = 25
12² = 12 x 12 = 144
13²= 13 x 13 = 169
and so 5² + 12² = 25 + 144 = 169 = 13²
7² + 24² = 25²
because 7² = 7 x 7 = 49
24² = 24 x 24 = 576
25² = 25 x 25 = 625
and so 7² + 24² = 49 + 576 = 625 = 25²
I will now work out the perimeter and area
Perimeter = a + b + c
Area = ½ x a x b
3, 4, 5
Perimeter = 12
Area = 6
5, 12, 13
Perimeter = 30
Area = 30
7, 24, 25
Perimeter = 56
Area = 84
I will now put these three terms in a table
Term Number
'n'
Length of shortest side
'a'
Difference between 'a'
Length of middle side
'b'
Length of longest side
'c'
Difference between 'b' and 'c'
Perimeter
Area
Sum Law (the sum of the interior angles of a triangle must sum to 180
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