UGC NET Questions (Paper – 1)

The area of a square is proportional to the square of its side, so if A₁:A₂ = 9:16, then (s₁²):(s₂²) = 9:16. Taking square roots of both sides gives s₁:s₂ = √9:√16 = 3:4. Thus, the side lengths must be in the ratio 3:4, which directly follows from the relationship between area and side for similar squares. No other option maintains this exact square–square root consistency.

Option A:
Option A is correct because it correctly applies the square root to the area ratio 9:16, converting it into a side ratio. Since area scales as the square of the side, this reverse operation is essential. The resulting ratio 3:4 is the only one consistent with both the given area ratio and the geometry of squares.

Option B:
Option B, 4:3, simply reverses the correct order and would imply that the square with area 9 units has the larger side, which contradicts the fact that 16 is greater than 9. If the second square has greater area, its side must be longer, not shorter, so 4:3 cannot be the correct side ratio.

Option C:
Option C, 9:16, repeats the area ratio rather than converting it to a side ratio and so ignores the square relationship. This would only be appropriate if areas themselves were being compared, not side lengths. Because the question explicitly asks for the ratio of sides, 9:16 is not valid here.

Option D:
Option D, 81:256, is the square of the given area ratio and would correspond to comparing higher powers of side lengths, not the sides themselves. It exaggerates the difference between the two squares and has no direct geometric justification in this context.