Question
The diagonals of a rhombus are in the ratio 3 :4. If the length of each side of the rhombus is 12.5 units, what is the length of the shorter diagonal?
This question was previously asked in
RRB NTPC 2025 Under Graduate CBT 1 Question Paper PDF (20-Jun-2026) (Shift 3)
The correct answer is
15 units
Let the diagonals be 3k and 4k. Using the rhombus side formula: \(\left(\tfrac{3k}{2}\right)^2+\left(\tfrac{4k}{2}\right)^2 = 12.5^2\).
\(2.25k^2+4k^2=156.25 \Rightarrow 6.25k^2=156.25 \Rightarrow k^2=25 \Rightarrow k=5\).
Shorter diagonal: \(3k=15\) units.
Hence, the length of the shorter diagonal is 15 units.
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