If s minus a s minus b s minus c s then the value of ........

Quantitative Aptitude (CDS) Simplification

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

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Explanation:

Given, (s − a) + (s − b) + (s − c) = s => 2s = (a + b + c)
$\therefore \: \frac{(s-a)^{2}+(s-b)^{2}+(s-c)^{2}+s^{2}}{a^{2}+b^{2}+c^{2}}$
$= \: \frac{3s^{2}+a^{2}+b^{2}+c^{2}-2s(a+b+c)+s^{2}}{a^{2}+b^{2}+c^{2}}$
$= \: \frac{4s^{2}+a^{2}+b^{2}+c^{2}-2s(2s)}{a^{2}+b^{2}+c^{2}}=\frac{a^{2}+b^{2}+c^{2}}{a^{2}+b^{2}+c^{2}}=1$