The diagonals of 2 squares M & N are in the ratio 2:1. The ratio of their areas is

Ratio of the lengths of the respective diagonals of two squares M and N is 2:1.

Let the ratio be x

So, length of respective diagonals of two squares M and N is 2x and x

Diagonal = $$\sqrt{2}a$$

In square M

2x = $$\sqrt{2}a$$

a = $$\frac{2x}{\sqrt{2}}$$

Area = $$\left(\frac{2x}{\sqrt{2}}\right)^2=\frac{4x^2}{2}=2x^2$$

In square N

x = $$\sqrt{2}a$$

a = $$\frac{x}{\sqrt{2}}$$

Area = $$\left(\frac{x}{\sqrt{2}}\right)^2=\frac{x^2}{2}$$

Required ratio = $$2x^2:\frac{x^2}{2}=4:1$$ .