Lagrangian:

where the function we want to minimize is actually

, but it's easy to see that

and

have critical points at the same vector

.
Derivatives of the Lagrangian set equal to zero:




Substituting the first three equations into the fourth gives


Solving for

, we get a single critical point at

, which in turn gives the least distance between the plane and (0, 2, 5) of

.
4/20 has the numbers 4 and 20 which can be simplified
2/10 is the same as 4/20 when you multiply both numbers by 2
and 1/5 is the simplest answer and is the same as 4/20 when both numbers are multiplied by 4
Hope this helps! :D