Two medians DM and EN of ΔDEF intersect each other at G at right angles. If EF = 20 cm and EN = 12 cm, then what is the length of DM?
Answer & explanation
Correct answer: option 3
In ΔDEF EN is the median.
So, EG : GN = 2 : 1
EN = 12 cm
EG : GN = 8 : 4
In ΔEGM
EM2 = GM2 + EG2
= 102 = GM2 + 82
= GM2 = 100 - 64
= GM = 6
DM is also a median
DG : GM = 2 : 1
DG = 2 × GM = 2 × 6 = 12 cm
DM = DG + GM = 12 + 6 = 18 cm