A) \[a+b\]
B) \[a-b\]
C) \[\frac{a-b}{2}\]
D) \[\frac{a+b}{2}\]
Correct Answer: B
Solution :
Area of rhombus \[=\frac{1}{2}{{d}_{1}}\times {{d}_{2}}=\frac{{{a}^{2}}-{{b}^{2}}}{2}\] Let second diagonal be = d \[\therefore \] \[\frac{1}{2}\]\[(a+b)\cdot d=\frac{{{a}^{2}}-{{b}^{2}}}{2}\] \[\Rightarrow \] \[(a+b)\,\,d={{a}^{2}}-{{b}^{2}}\] \[\Rightarrow \] \[d=\frac{({{a}^{2}}-{{b}^{2}})}{a+b}\] \[\Rightarrow \] \[d=(a-b)\]
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