In a ∆ABC, two medians AD and BE intersect at G at right angles. If AD = 18 cm and BE = 12 cm, then the length of BD is equal to:

Correct option is A

Given:

AD and BE is median.
​$$∠BGD=90^0$$ 

If AD = 18 cm and BE = 12 cm,​
Formula Used:
Median theorem = 2 : 1
Pythagoras theorem:
​$$H^2 = B^2+C^2$$​​
Solution:

BG : GE = 2 : 1 , AG : GD = 2 : 1 

BG = $$\frac{2}{3} BE$$ = $$\frac{2}{3}\times 12 = 8$$  cm 

GD = $$\frac{1}{3}AD = \frac{1}{2} \times 12 = 6$$  cm ​
Then, BG = 8 cm, GD = 6 cm
Now,
BGD is right angle triangle,
​$$BD^2 = GD^2 + BG^2$$​​
= 62 + 82
= 36 + 64
= 100
BD = √100 =10cm