A) 6
B) 9
C) 69
D) 96
E) 3
Correct Answer: C
Solution :
Area of \[\Delta ABD=2\Delta ACD\] \[\Rightarrow \] \[\frac{1}{2}\left| \begin{matrix} -3 & 4 & 1 \\ -1 & -2 & 1 \\ x & -4 & 1 \\ \end{matrix} \right|=2\times \frac{1}{2}\left| \begin{matrix} -3 & 4 & 1 \\ 5 & 6 & 1 \\ x & -4 & 1 \\ \end{matrix} \right|\] \[\Rightarrow \] \[\left| \begin{matrix} -3 & 4 & 1 \\ 2 & -6 & 0 \\ x+3 & -8 & 0 \\ \end{matrix} \right|=2\left| \begin{matrix} -3 & 4 & 1 \\ 8 & 2 & 0 \\ x+3 & -8 & 0 \\ \end{matrix} \right|\] \[\Rightarrow \] \[-16+6x+18=2(-64-2x-6)\] \[\Rightarrow \] \[6x+2=|-2(2x+70)|\Rightarrow x=69\]You need to login to perform this action.
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