For a cube as given, the Cl– ions are at the corners and one each in the face centre i.e. it is a ccp structure.
For a ccp structure 4r– = √2 a, The face diagonal = √2a
On the face diagonal there are only Cl– ions
4r– = √2 a or r– = 1.414 x 400/4 = 141.4 pm