A) \[48\sqrt{2}\,sq\,m\]
B) \[48\sqrt{3}\,sq\,m\]
C) \[48\,sq\,m\]
D) \[12\sqrt{2}\,sq\,m\]
E) \[12\sqrt{3}\,sq\,m\]
Correct Answer: A
Solution :
In \[\Delta ABE,\] \[\tan 60{}^\circ =\frac{AE}{AB}\Rightarrow AB=\frac{12}{\sqrt{3}}=4\sqrt{3}m\] and in \[\Delta ACE\] \[\tan 45{}^\circ =\frac{12}{AC}\Rightarrow AC=12\] \[\therefore \] \[BC=\sqrt{A{{C}^{2}}-A{{B}^{2}}}=\sqrt{144-48}=\sqrt{96}=4\sqrt{6}\] \[\therefore \]Area of rectangular field\[=AB\times BC\] \[=4\sqrt{3}\times 4\sqrt{6}\] \[=48\sqrt{2}\,sq\,m\]You need to login to perform this action.
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