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?

18 cm

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