Question

AD¯¯¯¯¯ ​ , BD¯¯¯¯¯ , and CD¯¯¯¯¯ are angle bisectors of the sides of △ABC . BE=12 m and BD=20 m

Answer 1

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