A) \[12\sqrt{6},4\sqrt{6}\]
B) \[12\sqrt{6},5\sqrt{6}\]
C) \[6\sqrt{6},4\sqrt{6}\]
D) \[6\sqrt{6},5\sqrt{6}\]
Correct Answer: A
Solution :
For \[\Delta \,ABC,\,\,a=6\,cm,\,\,b=5,\,\,c=7\,cm\] \[\therefore \] \[s=\frac{6+5+7}{2}=9\,cm\] \[\therefore \] Area of \[\Delta \,ABC=\sqrt{s(s-a)\,(s-b)\,(s-c)}\] \[=\sqrt{9\times (-6)\,(9-5)\,(9-7)}\] \[=\sqrt{9\times 3\times 4\times 2}\] \[=3\times 2\sqrt{6}=6\sqrt{6}\] Thus, area of quadrilateral \[=2\times \] Area of \[\Delta \,ABC\] \[=12\sqrt{6}\,sq\,cm\] Again, since \[AE=\frac{1}{2}AD=\frac{l}{2}\] Area of \[\Delta \,ABC=\frac{1}{2}\times BC\times AE\] or \[6\sqrt{6}=\frac{1}{2}\times 6\times \frac{l}{2}\] or \[l=4\sqrt{6}\]You need to login to perform this action.
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