If 2s = a + b + c, then the value of s(s - c) + (s - a) (s - b) is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{According to the question,}} \cr & {\text{If ,}}2s = a + b + c \cr & \Leftrightarrow s = \frac{{a + b + c}}{2} \cr & {\text{Let, }} \cr & a = 10 \cr & b = 10 \cr & c = 10 \cr & \because s = \frac{{a + b + c}}{2} \cr & \Rightarrow s = \frac{{10 + 10 + 10}}{2} \cr & \Rightarrow s = \frac{{30}}{2} \cr & \Rightarrow s = 15 \cr & \therefore s\left( {s - c} \right) + \left( {s - a} \right)\left( {s - b} \right) \cr & = 15\left( {15 - 10} \right) + \left( {15 - 10} \right)\left( {15 - 10} \right) \cr & = 75 + 25 \cr & = 100 \cr & {\text{Now check from option, }} \cr & {\text{Option 'A' }}ab = 10 \times 10 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 100\left( {{\text{Satisfied}}} \right) \cr} $$