Final answer:
In triangle EGB, the length of AG can be any positive value greater than 0 because the sum of the lengths of any two sides in a triangle is always greater than the length of the third side.
Step-by-step explanation:
Given that EB = 9 in triangle EGB, we need to find the length of AG.
In a triangle, the sum of the lengths of any two sides is always greater than the length of the third side.
So, EB + AG > EG and EB + AG > GB.
Since EB = 9 and EG = GB in an equilateral triangle, we can substitute these values into the inequalities: 9 + AG > 9 and 9 + AG > 9.
Simplifying, we get AG > 0.
Therefore, the length of AG is any positive value greater than 0.