The measures of CD = 33, EU = MU = 10.5, JD = 15.
In triangle CDE, the centroid U divides each median in a 2:1 ratio. This means that EM = 2MU and CU = 2UK.
We are given that EM = 21, so MU = EM/2 = 21/2 = 10.5
We are also given that UK = 12, so CU = 2UK = 2*12 = 24
To find the CD, we can use the following equation:
CD = CU + UD
Substituting the values we found, we get:
CD = 24 + 9 = 33
To find the EU, we can use the following equation:
EU = EM - MU
Substituting the values we found, we get:
EU = 21 - 10.5 = 10.5
To find JD, we can use the following equation:
JD = CU - UD
Substituting the values we found, we get:
JD = 24 - 9 = 15
Therefore, the measures of CD, EU, MU, and JD are 33, 10.5, 10.5, and 15, respectively.