Squares and their diagonals: Find the ratio of the area of a square to the area of the square built on its diagonal.
Aptitude
Area
Difficulty: Easy
Choose an option
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A1:2
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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: 1:2
Explanation
Introduction / Context:Building a new square on the diagonal of an original square scales the side by √2, so area doubles.
Given Data / Assumptions:Original square side = s; its diagonal = s√2, which becomes the side of the new square.
Concept / Approach:Areas: original = s^2; new = (s√2)^2 = 2s^2. Ratio original:new = 1:2.
Step-by-Step Solution:
Original area = s^2.New area = 2s^2.Ratio = s^2 : 2s^2 = 1 : 2.Verification / Alternative check:Let s = 10 → original 100; new 200 ⇒ 1:2.
Why Other Options Are Wrong:2:3, 3:1, 4:1 do not match the √2 side scaling effect on area.
Common Pitfalls:Using √2 for ratio directly; remember area scales with square of side.
Final Answer:1:2