CDS 2024 · PYQ · Data Sufficiency / Rhombus · medium
Question: What is the ratio of the lengths of diagonals of a rhombus? Statement-I: One diagonal of the rhombus is equal to its side. Statement-II: The longer diagonal of the rhombus is equal to √3 times its side.
A.If the Question can be answered by one of the Statements alone, but not by the other.
B.If the Question can be answered by either Statement alone.✓ Correct
C.If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
D.If the Question cannot be answered even by using both Statements together.
Explanation
If one diagonal = side s, then half-diagonal = s/2; the other half-diagonal = √(s² - s²/4) = s√3/2, so other diagonal = s√3. Ratio = 1 : √3. From Statement II, longer diagonal = s√3, so half longer = s√3/2; other half = √(s² - 3s²/4) = s/2; other diagonal = s. Ratio = 1 : √3. Either statement alone gives the ratio.
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