Quantitative Aptitude Ques 936

Question: The perimeter of a rhombus is 100 cm. If one of its diagonals is 14 cm, then the area of the rhombus is

Options:

A) $ 144cm^{2} $

B) $ 225cm^{2} $

C) $ 336cm^{2} $

D) $ 400cm^{2} $

Show Answer

Answer:

Correct Answer: C

Solution:

  • Side of rhombus $ =\frac{1}{2}\sqrt{d_1^{2}+d_2^{2}} $ Perimeter of rhombus $ =4\times \frac{1}{2}\sqrt{d_1^{2}+d_2^{2}} $

$ \therefore $ $ 2\sqrt{d_1^{2}+d_2^{2}}=100 $

$ \Rightarrow $ $ d_1^{2}+d_2^{2}=2500 $

$ \Rightarrow $ $ {{(14)}^{2}}+d_2^{2}=2500 $

$ \Rightarrow $ $ d_2^{2}=2340 $
$ \Rightarrow $ $ d _2=48 $

$ \therefore $ Area of rhombus $ =\frac{1}{2}\times d _1\times d _2 $ $ =\frac{1}{2}\times 14\times 48=336cm^{2} $

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