A) 2
B) 3
C) 4
D) 5
Correct Answer: A
Solution :
Let the fourth side be of ?d? length. We know that \[A{{B}^{2}}+B{{C}^{2}}-2AB.BC\cos {{60}^{o}}=A{{C}^{2}}\] \[=C{{D}^{2}}+D{{A}^{2}}-2CD.DA\,\,\cos {{120}^{o}}\] (by cosine rule) or \[4+25-2.\,2.\,5.\frac{1}{2}=9+{{d}^{2}}+3d\] Þ \[{{d}^{2}}+3d-10=0\Rightarrow d=-5\]or \[d=2\]; \ \[d=2\].You need to login to perform this action.
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