Question

Prove the Pythagorean theorem using diagrams and the following facts: the area of a square with side s is s^2 and the area of a triangle with base b and height h is 1/2bh

Answer 1

The area of the ouside square is (a+b)^2
another way to find the area is to find the are of each triangle add them up and then add the area of the inner box to that

so

(a+b)^2=4(1/2)ba+c^2

a^2+2ab+b^2=2ab+c^2

a^2+b^2=c^2