Tiling Into Slanted Rectangles

 This is seen as a possible follow on from Tiles in the Garden.

This activity takes "Tiles in the Garden", much further. We can keep the main ideas the same - 

• Square tiles
• A corner of a tile at each corner of the rectangle
• The ability to slice a tile into parts so as to use each part

Image

So this one used $26$ and the slope was generated by going along $1$ and up $5$.

This time let's put on a limit of using less than $100$ tiles.

What sizes of rectangles could be filled obeying the three rules?

How many tiles for each rectangle you find?

Are there any numbers of tiles between $10$ and $100$ for which there cannot be a rectangle?