Answer/Step-by-step explanation:
Problem 1:
E is the centroid of the triangle.
Centroid theorem states that the centroid is ⅔ of the distance of each vertex to the midpoint of the side opposite each vertex.
This implies that:
AE = ⅔(AD)
AE = 21
Therefore:
21 = ⅔(AD)
3*21 = 2(AD)
(3*21)/2 = AD
31.5 = AD
AD = 31.5
Problem 2: Apply the centroid theorem. Thus:
DE = ⅓(AD)
DE = 12
Therefore,
12 = ⅓(AD)
12*3 = AD
36 = AD
AD = 36
