• # question_answer If ${{c}^{2}}={{a}^{2}}+{{b}^{2}},$ $2s=a+b+c,$ then $4s\,(s-a)\,\,(s-b)\,\,(s-c)=$ A) ${{s}^{4}}$ B) ${{b}^{2}}{{c}^{2}}$ C) ${{c}^{2}}{{a}^{2}}$          D) ${{a}^{2}}{{b}^{2}}$

 ${{c}^{2}}={{a}^{2}}+{{b}^{2}}$           $\Rightarrow$$\angle \,C=\frac{\pi }{2}$ $\therefore$$\Delta =\frac{1}{2}ab\sin C=\frac{1}{2}ab$$\Rightarrow$$\sqrt{s\,(s-a)\,\,(s-b)\,\,(s-c)}=\frac{1}{2}ab$$\Rightarrow$$4s\,(s-a)\,\,(s-b)\,\,(s-c)={{a}^{2}}\,{{b}^{2}}.$