The area of square is 100m². A new square is inscribed in such a way that the length of its diagonal is \(\sqrt {2}\) times of the given square. Then the area of the new square formed is?

200

Area of square = 100 m2

side of square = 10 m

diagonal of square = \(10\sqrt {2}\)

Diagonal of new square = \(\sqrt {2}(10\sqrt {2})m = 20 m\)

side of new square = \(\frac{20}{\sqrt {2}}=\frac{20\sqrt {2}}{2}=10\sqrt {2}m\)

Area of new square = \((10\sqrt {2})^2=100×2=200m^2\)