Answer:
We know that, \[{{\left( a+b \right)}^{2\text{ }}}=\text{ }{{a}^{2}}+{{b}^{2}}+2ab~~\] Here, \[a+b\text{ }=25,\text{ }{{a}^{2}}+{{b}^{2}}=225~~\] \[\Rightarrow \] \[{{(25)}^{2}}=225+2ab\] \[\Rightarrow \] 625 = 225 + 2ab \[625-225=2ab\] \[\Rightarrow \,\] 400 = 2ab \[\Rightarrow \,\] \[ab=\frac{400}{2}\] \[\Rightarrow \,\]ab = 200
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