Pattern A Block Around Oval

Hello -

I was wondering if it is possible to pattern a block (green profile in attached PNG) around a slot (red profile in attached PNG).  The knowns are the number of blocks we would like, the pitch between each block, and the height of the oval.  What we need to figure out is how wide the oval needs to be.

Is there an easy way to model/sketch this?  Thanks in advance!

SolidworksSketching