Quantitative Aptitude Ques 2241
Question: Two medians AD and BE of $ \Delta ABC $ intersect at G at right angles. If $ AD=9cm $ and $ BE=9cm $ then the length of BD, in cm, is
Options:
A) 10
B) 6
C) 5
D) 3
Show Answer
Answer:
Correct Answer: C
Solution:
- $ AD=9cm $ $ \because $ A centroid divides the median in the ratio 2: 1.
$ \therefore $ $ GD=\frac{1}{3}\times 9=3cm $
[ $ \because $ point of intersection of median]
and $ BG=\frac{2}{3}\times BE $
$ \Rightarrow $ $ BG=\frac{2}{3}\times 6=4cm $
Now, in $ \Delta BDG $ by Pythagoras theorem,
$ BD^{2}=BG^{2}+GD^{2} $
$ \therefore $ $ BD=\sqrt{3^{2}+4^{2}}=\sqrt{9+16} $
$ \Rightarrow $ $ BD=\sqrt{25}=5cm $
BETA
