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} $
BETA
