How to bend a single shape along a path?

[fanbrahms]

Hello everyone,

I've come across this problem when trying to connect two outline letters. 

In the attached picture it is shown, as I want the selected rectangular shape to follow the drawn line path, without distorting the selected shape's proportions, connecting the A to the K.

[Met1]

I'm not really sure what you're asking - you want the width of the right hand K foot to taper then widener to match the left hand A foot, right? - if so, use the width tool on one of the paths you've already drawn (delete the other).

If that's not what you mean, you'll have to explain it more precisely...

[Monika Gause]

An art brush would do that. Make the shape into an art brush and apply it to the path.