A) \[5\sqrt{2}\,cm\]
B) 5 cm
C) 6 cm
D) \[2\sqrt{5}\,cm\]
Correct Answer: A
Solution :
\[\therefore \] \[~x+y+\text{ }z=12\] ? (i) \[\therefore \] \[2(xy+yz+zx)=\text{9}4\] ? (ii) \[\therefore \] \[~{{(x+y+\text{ }z)}^{2}}={{x}^{2}}+{{y}^{2}}+\text{ }{{z}^{2}}+2xy+2yz+2zx\] \[\Rightarrow \] \[~144={{x}^{2}}+{{y}^{2}}+\text{ }{{z}^{2}}+94\] \[\Rightarrow \] \[~{{x}^{2}}+{{y}^{2}}+\text{ }{{z}^{2}}=144-94=50\] \[\therefore \] Maximum length of stick \[=~\sqrt{{{x}^{2}}+{{y}^{2}}+\text{ }{{z}^{2}}}\] \[=\sqrt{50}=5\sqrt{2}\,cm\]
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