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)?
Aptitude
Area
Difficulty: Easy
Choose an option
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A2:1
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B2:3
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C3:1
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D4:1
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ENone of these
Answer
Correct Answer: 4:1
Explanation
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:
Let diagonal of small square = d; area ∝ d^2.Larger diagonal = 2d ⇒ area ∝ (2d)^2 = 4d^2.Ratio = 4d^2 : d^2 = 4 : 1.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