In △ ABC, D and E are the mid-points of sides BC and AC, respectively. AD and BE intersect at G at right angle.If AD = 18 cm and BE = 12 cm, then the length of DC (in cm) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 10
As one can see that, AD and BE act as a median so G must be a centroid.
GD = 1/3 of AD = 1/3 of 18 = 6cm.
BG = 2/3 of 12 = 8cm.
Now in △ BGD, by using Pythagoras' theorem
BG2 + DG2 = BD2
64 + 36 = BD2
BD = 10.
BD = DC = 10 cm.