Quantitative Aptitude Ques 879
Question: If two adjacent sides of a rectangular parallelepiped are 1 cm and 2 cm and the total surface area of the parallelepiped is $ 22cm^{2}, $ then the diagonal of the parallelepiped is
Options:
A) $ \sqrt{10}cm $
B) $ 2\sqrt{3}cm $
C) $ \sqrt{14}cm $
D) $ 4cm $
Show Answer
Answer:
Correct Answer: C
Solution:
- Let the third side of the rectangular parallelepiped be x. Total surface area of parallelepiped $ =22 $
$ \Rightarrow $ $ 2(lb+bh+lh)=22 $
$ \Rightarrow $ $ 2(x\times 1+1\times 2+2\times x)=22 $
$ \Rightarrow $ $ 3x+2=11 $
$ \Rightarrow $ $ 3x=11-2=9 $
$ \Rightarrow $ $ x=\frac{9}{3}=3cm $
$ \therefore $ Diagonal of parallelepiped $ =\sqrt{l^{2}+b^{2}+h^{2}} $ $ =\sqrt{3^{2}+2^{2}+1^{2}} $ $ =\sqrt{9+4+1}=\sqrt{14}cm $
BETA
