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December 20, 2014

December 20, 2014

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

- geometry -
**Steve**, Thursday, November 24, 2011 at 7:18pmWithout 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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