A) 8/3
B) 16/3
C) 32/3
D) 64/3
Correct Answer: D
Solution :
None of the given option is correct. Median divides a triangle into two parts of equal area. So, we have to find area of one triangle. Given, AD = 4 and SD = DC We know that the centroid G divides the line AD in the ratio 2 : 1 . \[AG=\frac{8}{3}\] and \[DG=\frac{4}{3}\] In \[\Delta ABG\], \[\tan \frac{\pi }{3}=\frac{AG}{BG}\] \[\Rightarrow \] \[BG=AG\cot \frac{\pi }{3}\] \[BG=\frac{8}{3}\times \frac{1}{\sqrt{3}}=\frac{8}{3\sqrt{3}}\] Area of MDS \[\Delta ADB=\frac{1}{2}\times BG\times AD\] \[=\frac{1}{2}\times \frac{8}{3\sqrt{3}}\times 4=\frac{16}{3\sqrt{3}}\] Since, median divide a triangle into two triangles of equal area. Therefore, Area of \[\Delta ABC=2\times \] Area of \[\Delta ADB\] \[=2\times \frac{16}{3\sqrt{3}}=\frac{32}{3\sqrt{3}}\] None of the given option is correct.You need to login to perform this action.
You will be redirected in
3 sec