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Since $AD$ is the median, $D$ is the mid-point of $BC$.

$∴$ coordinates of point $D=$ $(20+6 ,24+0 ,20+0 )=(3,2,0)$

$AD=$ $(0−3)_{2}+(0−2)_{2}+(6−0)_{2} =9+4+36 =49 =7$

Since $BE$ is the median, $E$ is the mid-point of $AC$.

$∴$ coordinates of point $E=$ $(20+6 ,20+0 ,26+0 )=(3,0,3)$

$BE=$ $(3−0)_{2}+(0−4)_{2}+(3−0)_{2} =9+16+9 =34 $

Since $CF$ is the median, $F$ is the mid point of $AB$.

$∴$ coordinates of point $F=$ $(20+0 ,20+4 ,26+0 )=(0,2,3)$

Length of $CF=$ $(6−0)_{2}+(0−2)_{2}+(0−3)_{2} =36+4+9 =49 =7$

Thus the lengths of the medians of $△ABC$ are $7,34 $ and $7$ units.

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