The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon?

Answer 1

Without loss of generality, assume a square of side 1. Now, if we cut off a piece of length x from each end of the side, then the diagonal of the cut corner will be x√2.

To make things come out right, the two cuts and the remaining middle piece add up to 1:

1 - 2x = x√2
1 = (2+√2)x
x = 1/(2+√2) = 1 - 1/√2 = 0.2928

Check:
1 - 2x = .4142
.2928√2 = .4142

So, I've solved for x. What is the side length?

Answer 2

Let x be the side of square and y be the side of octagon their for the relation between y and x is:
y=x/1+2^1/2
Theirfore y=.828