What is the minimum possible perimeter of a triangle two of whose sides are along the $x$- and $y$-axes and such that the third contains the point $(1,1)$?

Here's what I think :

This will be a right triangle with legs = 2 and hypotenuse = 2sqrt (2)

Minimum perimeter = 2 + 2 + 2sqrt (2) = 4 + 2sqt (2)