Squares – Compare areas when one square has double the diagonal of the other: Two squares are given. The diagonal of the first is exactly twice the diagonal of the second. What is the ratio of their areas (larger : smaller)?

Introduction / Context:The area of a square is proportional to the square of its side. Its diagonal is side * √2, so area is also proportional to the square of the diagonal.

Given Data / Assumptions:

• Square A has diagonal 2d; Square B has diagonal d.
• We need area(A) : area(B).

Concept / Approach:If diagonal doubles, area scales by (2)^2 = 4, because Area ∝ diagonal^2.

Step-by-Step Solution:

Verification / Alternative check:Take a concrete example: if d = √2, side = 1, area = 1. If 2d = 2√2, side = 2, area = 4 ⇒ ratio 4:1.

Why Other Options Are Wrong:2:1, 3:1 imply linear scaling; area scales quadratically with diagonal.

Common Pitfalls:Mistaking diagonal or side as linearly linked to area; forgetting square-law scaling.

Final Answer:4:1