The diagonals of two squares area in the ratio 2 : 5, their area will be in the ratio of:

\(\sqrt {2}\) : \(\sqrt {5}\) 2 : 5 4 : 25 9 : 25

4 : 25

Diagonal of square = \(\sqrt {2}\) side ⇒ side = \(\frac{diagonal}{\sqrt {2}}\) ATQ, Ratio of diagonal = 2 : 5, Ratio of side = \(\frac{2}{\sqrt {2}}\) : \(\frac{5}{\sqrt {2}}\) = 2 : 5 ⇒ Ratio of area = Square of ratio of sides = 22 : 52 = 4 : 25