The diagonals of two squares are in the ratio of 3:2.Find the ratio of their areas ?

The correct answer is: ∴ Ratio of the areas of the 2 squares = 2.25 : 1.

Step-by-step solution:-
Let Diagonal 1 & Diagonal 2 be the diagonals of the 2 squares given in the question.
∴ Diagonal 1 : Diagonal 2 = 3 : 2
Let x be the common factor
∴ Diagonal 1 = 3x ….................................... (Equation i)
& Diagonal 2 = 2x ….................................... (Equation ii)
For Square 1-
   Area 1 = 1/2 (diagonal 1)²
∴ Area 1 = 1/2 (3x)2 ................................... (From Equation i)
∴ Area 1 = 1/2 × 9x²
∴ Area 1 = 4.5 × x²
∴ Area 1 = 4.5 x^{2 .}..................................... (Equation iii)
For Square 2-
   Area 2 = 1/2 (diagonal 2)²
∴ Area 2 = 1/2 (2x)^{2 ...}................................ (From Equation ii)
∴ Area 2 = 1/2 ×4x²
∴ Area 2 = 2 × x²
∴ Area 2 = 2 x² ...................................... (Equation iv)
Ratio of the Areas of the 2 squares = Area of Square 1 / Area of Square 2
∴ Ratio of the Areas of the 2 squares = 4.5 x² / 2 x² ........................................... (From Equations iii & iv)
∴ Ratio of the Areas of the 2 squares = 2.25: 1