Posted by Lian on Thursday, November 24, 2011 at 5:44am.
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?
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