question_answer

Two median AD and BE of \[\Delta ABC\] interest at G at right angles. If AD = 9 cm and BE = 6 cm, then the length of BD (in cm), is

A) 10                                

B) 6

C) 5         

D) 3

Correct Answer: C

Solution :

    

Given, \[AD=9\,cm\]

\[\because \] A centroid divides the median in the ratio 2: 1.

\[\therefore \]      \[GD=\frac{1}{3}\times 9=3\,cm\]

[\[\because \] point of Intersection of median]

and       \[BG=\frac{2}{3}\times BE\]\[\Rightarrow \]\[BG=\frac{2}{3}\times 6=4\,cm\]

Now, in \[\Delta BDG\] by Pythagoras theorem,

\[B{{D}^{2}}=B{{G}^{2}}+G{{D}^{2}}\]

\[\Rightarrow \]   \[BD=\sqrt{{{3}^{2}}+{{4}^{2}}}=\sqrt{9+16}\]

\[\Rightarrow \]   \[BD=\sqrt{25}=5\,cm\]