Question

A square is of area $200sq.m.$ A new square is formed in such a way that the length of its diagonal is $\sqrt{2}$ times of the diagonal of the given square. Then the area of the new square formed is

• A. $200\sqrt{2}sq.m$
• B. $400\sqrt{2}sq.m$
• C. $400sq.m$
• D. $800sq.m$

Answer 1

The correct option is C $400sq.m$

According to question,

Side lenght of square=$\sqrt{200}=10\sqrt{2}m$

So, lenght of its diagonal $=10\sqrt{2}\times \sqrt{2}=20m$

Length of diagonal of new square $=20\times \sqrt{2}m$

So, side length of new square $=\frac{20\sqrt{2}}{\sqrt{2}}=20m$

Hence, area of new square $=20m\times 20m=400m^2$