The diagonal of the larger square is \(\sqrt{1+1}\) inches = \(\sqrt{2}\) inches

The area of the larger square is 1 square inches

Let the side of smaller square be a

The area of the smaller square is \(a^2\) square inches = \(\frac{2}{3}\) * area of larger square = \(\frac{2}{3} * 1\)

=> a = \(\sqrt{\frac{2}{3}}\)

length of diagonal of smaller square is \(\sqrt{a^2 + a^2}\) = \(\sqrt{2a^2}\) = \(\sqrt{\frac{4}{3}}\)

Length of diagonal of larger square - Length of diagonal of smaller square = \(\sqrt{2} - \sqrt{\frac{4}{3}}\) = \({\sqrt{2} - \frac{2\sqrt3}{3}\)

Hence

option A
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