Answer
$\sqrt {29}, 2\sqrt 5, \sqrt {17}$.
Work Step by Step
Step 1. Use the given information, we have the coordinates of the Midpoint of BC as $(\frac{6+4}{2},\frac{0+4}{2})$ or $(5,2)$. Thus the length of the Median from vertex-A is $d_1=\sqrt {(5-0)^2+(2-0)^2}=\sqrt {29}$,
Step 2. The coordinates of the Midpoint of AC are $(\frac{0+4}{2},\frac{0+4}{2})$ or $(2,2)$. Thus the length of the Median from vertex-B is $d_2=\sqrt {(6-2)^2+(0-2)^2}=\sqrt {20}=2\sqrt 5$,
Step 3. The coordinates of the Midpoint of AB are $(\frac{0+6}{2},\frac{0+0}{2})$ or $(3,0)$. Thus the length of the Median from vertex-C is $d_3=\sqrt {(4-3)^2+(4-0)^2}=\sqrt {17}$.
