Answer to Question #90732 in Economics for Unknown287159

Question

Prove the pythagorus theorem.

Answer 1

Let QR = a, RP = b and PQ = c. Now, draw a square WXYZ of side (b + c). Take points E, F, G, H on sides WX, XY, YZ and ZW respectively such that WE = XF = YG = ZH = b.

Then, we will get 4 right-angled triangle, hypotenuse of each of them is ‘a’: remaining sides of each of them are band c. Remaining part of the figure is the 

square EFGH, each of whose side is a, so area of the square EFGH is a².

Now, we are sure that square WXYZ = square EFGH + 4 ∆ GYF

or, (b + c)² = a² + 4 ∙ ¹/₂ b ∙ c

or, b² + c² + 2bc = a² + 2bc

or, b² + c² = a²