ANSWER
(a) DE is the shortest side of the median.
[tex]DE=\frac{1}{3}CE[/tex](b) DE = 5
EXPLANATION
The centroid is the point of congruence of all the medians of a triangle. The distance from the vertex to the centroid is 2/3 the lenght of the median and the distance from the centroid to the side of the triangle is 1/3 the lenght of the median.
DE is the segment from the centroid to the side of the triangle, so:
[tex]DE=\frac{1}{3}CE[/tex]If CE = 15, then:
[tex]DE=\frac{1}{3}\times15=5[/tex]