He would need a minimum of 140 tiles, to include all three arrangements (7 rectangular shapes).
Example: BLUE: 2 of 2×10, 1 of 1×20 and 4 of 4×5=40+20+80=140; or RED: 1 of 4×5, 4 of 1×20 and 2 of 2×10=20+80+40=140.
The reason for this minimum value of 7 20-tile rectangles is this:
1×4=2×2=4×1, that is, 1 of 4×5=2 of 2×10=4 of 1×20, or it takes 2 of the width of the 2×10 and 4 of the width of 1×20 to make up the width of the 4×5 shape. 4+2+1=7 and 7 shapes each with an area of 20 tiles make 140 tiles. Similarly, 1×20=2×10=4×5, that is, 1 of 1×20=2 of 2×10=4 of 5×4, or it takes 2 of the length of the 10×2 and 4 of the length of 5×4 to make up the length of the 20×1 shape. Again, this comes to 7 shapes.
There are several ways of arranging the 7 shapes to fit together to form a rectangular design.