Pythagoras formula

  In any Right angle  Triangle of side a,b,c        How????

                            Consider a square of side c and draw a four right angle triangle on each side in such a way that side of square is hypotenuse of a triangle as shown in fig,

                                             

                Now outer square is of length a+b so its area is . Here area of inner square of side c is and as we know area of trigle is 1/2*height*base. In this case the area of triangle becomes . so area of such four triangle is .

       Now area of outer square =  the sum of areas of inner sqaure and  four triangles. 

 It gives,

        

                                    Hence proved.