Squares — Diagonal Ratio to Area Ratio: The diagonals of two squares are in the ratio 3 : 2. Find the ratio of their areas (larger : smaller).

Introduction / Context:For squares, the diagonal is proportional to the side and area scales with the square of any linear dimension. This item checks proportional reasoning by connecting a diagonal ratio directly to an area ratio without computing actual side lengths.

Given Data / Assumptions:

• Two squares with diagonal ratio d1 : d2 = 3 : 2
• Square properties: d = s * √2; area A = s^2 = d^2 / 2
• We need the ratio of areas (larger : smaller)

Concept / Approach:Because A ∝ d^2 for squares, the ratio of areas equals the square of the ratio of diagonals. No numeric side computation is necessary; simply square each term in the diagonal ratio and simplify the fraction to obtain the area ratio.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 9 : 2, 9 : 5, 9 : 7 do not arise from squaring 3 : 2.
• 4 : 3 inverts the order (smaller : larger).

Common Pitfalls:

• Using 3 : 2 directly for area instead of squaring.
• Swapping larger and smaller by mistake.

Final Answer:9 : 4.