beyond pythagoras

Maths GCSE Coursework

Beyond Pythagoras

Aim
The aim of this coursework is to investigate the relationship between the lengths of the three sides of right angle triangles, the perimeters and the areas of the triangles.

For any right-angled triangle the (shortest side) ²+ (middle side) ² will equal to the (longest side) ². I have represented this in the simple formula below.

a ²+b ²=c ²

The numbers 3, 4 and 5 satisfy the equation. This is because
3² + 4² = 5²

= (3 x 3) + (4 x 4) = (5 x 5)
9 + 16 = 25

The overall formula for all Pythagorean triples is :-

(shortest side) ²+(middle side) ²=(longest side) ²



1.a) I will use the set of numbers 5,12 and 13 to check this formula.

(shortest side) ²+( middle side) ²=(longest side) ²
5² + 12² = 13²
25 + 144 = 169
This set...