Can somebody explain me step 3, in the following link - here
1 Answer
$\begingroup$You want to take the rectangle on the left, with sides $a$ and $b$, and cut it with scissors into pieces that can then be rearranged into a square with side length $y$. The picture on the left shows the different scissor cuts made, and then four ensuing regions. To be formal about it, they specify the values for $x$ and $y$.
The important part of the argument is to show that if you actually rearrange the pieces as promised, you do indeed end up with a square (all sides are the same length), and that the length of that side is $y$. It is easy to see that the bottom and top of the "square" constructed have length $y$ (Pythagorean theorem), and the the length of the sides of the "square" are the same. What remains is to show that the length of either side of the "square" is equal to $y$, and that is exactly the algebraic equation presented.
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