Step 1

Given three vertices of the triangle are

$A(0,0,6),\:B(0,4,0)\:and\:C(6,0,0)$

Mid point of $AB$ is given by $D\big(\large\frac{0+0}{2},\frac{0+4}{2},\frac{6+0}{2}\big)$

$=D(0,2,3)$

Step 2

Mid point of $BC$ is given by $E\big(\large\frac{0+6}{2},\frac{4+0}{2},\frac{0+0}{2}\big)$

$=E(3,2,0)$

Step 3

Mid point of $AC$ is given by $F\big(\large\frac{0+6}{2},\frac{0+0}{2},\frac{6+0}{2}\big)$

$=F(3,0,3)$

Step 4

The three medians are $CD,\:AE\:and\:BF$

median $CD=\sqrt {(6-0)^2+(0-2)^2+(0-3)^2}=\sqrt {49}=7$

median $AE=\sqrt {(0-3)^2+(0-2)^2+(6-0)^2}=\sqrt {49}=7$

median $BF=\sqrt {(0-3)^2+(4-0)^2+(0-3)^2}=\sqrt {34}$