A) 5
B) 7
C) 8
D) 10
Correct Answer: B
Solution :
\[\Delta =10\sqrt{3}\] \[\Delta =\frac{1}{2}ab\sin C\Rightarrow ab=20\sqrt{3}\frac{2}{\sqrt{3}}=40\] ?.. (i) Also \[a+b+c=20\]or \[a+b=(20-c)\] Now, \[\cos C=\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2ab}=\frac{1}{2}\] Þ \[{{a}^{2}}+{{b}^{2}}-{{c}^{2}}=ab\] Þ \[{{(a+b)}^{2}}-{{c}^{2}}=ab+2ab=3ab\] Þ \[{{(20-c)}^{2}}-{{c}^{2}}=3(40)\] Þ \[-40c+400=120\Rightarrow c=7\].
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