What is length of diagonal of the central 'square?

Prove by indirect method "the length of a diagonal of a square is not equal in length to the length of any of?

• prove by indirect method "the length of a diagonal of a square is not equal in length to the length of any of the sides of the square How do I do this with the statement and ...show more

• Answer:

  Suppose that the diagonal of a square measures the same length as one of the sides. So the sides measure s and the diagonal measures s. But the diagonal of a square is always sqrt(2) (square root of two) times longer than any side length (note the Pythagorean theorem) thus s = s*sqrt(2). Subtracting s from both sides gives 0 = s*sqrt(2) - s = (sqrt(2) -1)s, and dividing both sides by sqrt(2) - 1 gives s = 0. So the side length and diagonal are zero, and it really wouldn't be a square. This is proof by contradiction- assuming something is true and then showing it leads to a statement which is obviously not true.