A) \[\sqrt{91}\]
B) \[3\sqrt{3}\]
C) 5
D) None of these
Correct Answer: A
Solution :
Since, angles of \[\Delta \] are in AP. Let, third side is x. \[\Rightarrow \,\,(\alpha -\delta )+\alpha +(\alpha +\delta )=180{}^\circ \Rightarrow \alpha =60{}^\circ \] Use cosine law in \[\Delta ABC\] \[\cos 60{}^\circ =\frac{{{(10)}^{2}}+{{(9)}^{2}}-{{x}^{2}}}{2.(10).(9)}\Rightarrow \frac{1}{2}=\frac{181-{{x}^{2}}}{2.(90)}\] \[\Rightarrow \,{{x}^{2}}=91\Rightarrow x=\sqrt{91}.\]
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