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SSC Quantitative Aptitude Mensuration Question Bank Mensuration-I (II)

  • question_answer
    The perimeter of a rhombus is 60 cm and one of its diagonal is 24 cm. The area (in sq cm) of the rhombus is     [SSC CGL Tier II, 2015]

    A) 206

    B) 216

    C) 432

    D) 108

    Correct Answer: B

    Solution :

    [b] Let the length of second diagonal of rhombus be d cm. thus,                         \[\sqrt{{{d}^{2}}+{{24}^{2}}}=2\times \left( \frac{60}{4} \right)\]             \[\Rightarrow \]   \[\sqrt{{{d}^{2}}+576}=2\times 15\] \[\Rightarrow \]   \[{{d}^{2}}+576=4\times 225\] \[\Rightarrow \]   \[{{d}^{2}}=900-476\]\[\Rightarrow \]\[{{d}^{2}}=324\] \[\therefore \]      \[d=18\,cm\] Then, area of rhombus \[=\frac{1}{2}\times \]Multiplication of diagonals \[=\frac{1}{2}\times 18\times 24=9\times 24=216\,sq\,cm\]


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