Hearth Rug

Mrs. Hobson's boy had an accident when playing with the fire, and burnt two of the corners of a pretty hearthrug. 
The damaged corners have been cut away, and it now has the appearance and proportions shown in my diagram. 

How is Mrs. Hobson to cut the rug into the fewest possible pieces that will fit together and form a perfectly square rug? 
It will be seen that the rug is in the proportions 36 × 27 (it does not matter whether we say inches or yards), and each piece cut away measured

See answer

Math Genius