Final answer:
To find the length of AE, we need to find the length of AG and then divide it by three. However, we do not have enough information to determine the length of AE accurately.
Step-by-step explanation:
The length of AE can be found by using the properties of a centroid. In a triangle, the centroid is the point of intersection of the medians. The median from vertex A to side BC is a line segment that connects A to the midpoint of BC, which we'll call D. The centroid, G, is the point of intersection of the medians, so in this case, AG is one of the medians. Since G is the centroid, AG is twice as long as GE, and DG is twice as long as GD. Therefore, in triangle AGD, AE is one-third of AG. So, to find the length of AE, we need to find the length of AG and then divide it by three.
We do not have enough information to find the length of AG in this question, as the specific dimensions of triangle ABC are not given. Therefore, without more information, we cannot determine the length of AE accurately.