question_answer

If \[({{a}^{2}}+{{b}^{2}})\,\,({{m}^{2}}+{{n}^{2}})={{(am+bn)}^{2}},\]then which one of the following statements is true?

A)  \[\frac{a}{m}=\frac{b}{n}\]

B)  \[\frac{a}{n}=\frac{b}{m}\]              

C)  \[ab=mn\]                

D)  \[a+b=m+n\]

E)  None of these