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

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