Since triangle BDE is right, we can check it for special rules: BD is hypotenuse = 20, and BE = 12, both divisible by 4: get 5 and 3... so it's a 3-4-5 special right triangle, the 4×4 = 16 m for side DE.
Since AD bisects angle A, I think then side DG should be congruent with DG. So then
DG = 16 m
