Answer:
EG = 26
Step-by-step explanation:
We use the angle-bisector theorem here
The theorem is that given an angle that is bisected in a triangle, it splits the opposite side into two parts, with the ratio of the sides facing the angle and the adjoining leg equal for the two bisections
So, we have this as;
EF/ED = GD/FG
x/24 = x+10/54
54(x) = 24)x + 10)
54x = 24x + 240
54x-24x = 240
30x = 240
x = 240/30
x = 8
But;
EG = EF + FG
EG = x + x + 10 = 2x + 10
EG = 2(8) + 10
EG = 16 + 10 = 26
