Quantitative Aptitude Ques 2287

Question: If $ a+b+c=2s, $ then the value of $ {{(s-a)}^{2}}+{{(s-b)}^{2}}+{{(s-c)}^{2}} $ will be

Options:

A) $ s^{2}+a^{2}+b^{2}+c^{2} $

B) $ a^{2}+b^{2}+c^{2}-s^{2} $

C) $ s^{2}-a^{2}-b^{2}-c^{2} $

D) $ 4s^{2}-a^{2}-b^{2}-c^{2} $

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ a+b+c=2,s $
    $ \Rightarrow $ $ s=\frac{a+b+c}{2} $ By expanding the expression, $ {{(s-a)}^{2}}+{{(s-b)}^{2}}+{{(s-c)}^{2}} $ $ =s^{2}+a^{2}-2as+s^{2}+b^{2}-2bs+s^{2}+c^{2}-2cs $ $ =3s^{2}+a^{2}+b^{2}+c^{2}-2s(a+b+c) $ $ =3s^{2}+a^{2}+b^{2}+c^{2}-2s,(2s) $ $ =3s^{2}+a^{2}+b^{2}+c^{2}-4s^{2} $ $ =a^{2}+b^{2}+c^{2}-s^{2} $
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