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By property of 45-90-45 triangle we get the sides of small triangle= 1/√2
Hence area of small sqr=1/2
Ar of large sqr= 2*1/2=1
Side of large sqr=1
Therefore difference in length of sides for large and small sqr= 1-1/√2 = (√2-1)/√2= √2*(√2-1)/√2*√2= (2-√2)/2
IMO A

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