Investigating the Relationship Between the Lengths, Perimeter and Area of a Right Angle Triangle

2080 Words5 Pages

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

More about Investigating the Relationship Between the Lengths, Perimeter and Area of a Right Angle Triangle

Open Document