geometry
posted by Lian .
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?

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? 
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
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Maths (Proof)
An octagon is formed by joining the points (7,0), (5,5), (0,7), (5,5), (7,0), (5,5), (0,7), (5,5) and (7,0). The octagon is regular. I have used proof by exhaustion and got that all sides are square root of 29. Then sketched …