Quantitative Aptitude Ques 500
Question: 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
Options:
A) 10
B) 6
C) 5
D) 3
Show Answer
Answer:
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,
$ BD^{2}=BG^{2}+GD^{2} $
$ \Rightarrow $ $ BD=\sqrt{3^{2}+4^{2}}=\sqrt{9+16} $
$ \Rightarrow $ $ BD=\sqrt{25}=5,cm $
BETA
