This is a total OverHeadTramission....I could not understand wat this means....I would appreciate if you can explain this also....

Posted by Murali on March 20, 2007 at 11:48 AM IST #

Simple. Look at the first square, on the left. It has two smaller squares inside it. Each of those smaller squares is the "square of one leg of a right triangle", because one side of the smaller squares is the leg of one of the 4 identical right triangles in the larger square. With me so far? So, together the area of the two small squares is "the sum of the squares of the legs of a right triangle." Now look at the large square on the right. It has the four small right triangles arranged inside of it. The smaller square inside this one has as its side the hypotenuse of those right triangles, so its area is "the square of the hypotenuse". If we look at the two large squares, we see that both of them has as its side each of the two legs of the right triangles, so the two larger squares must be the same size. Now consider what is left from both large squares after we take away the 4 right triangles. From the left square we are left with the two smaller squares, and from the right square we are left with the single square. Since the area of the 4 triangles is the same, the area of the remaining pieces must be the same. Thus we have shown that the area of the two squares is equal to the area of the single square and that "the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse." QED.

Posted by Brian Utterback on March 20, 2007 at 11:25 PM IST #