# Two rectangles for the price of one

Can you re-arrange these rectangles to form another rectangle, but with different dimensions (dimensions commute in this case)?

• Do you have to stay within the defined grid coordinate system (meaning you can't split up grid cells)? – Aranlyde May 15 at 7:13
• A and 1 can be considered to be the same length. The beige right hand cell is 2*10, but can be rotated to 10*2. – JMP May 15 at 7:15

No. The rectangle has an area of $$75$$ square units. The only other rectangle with integer sides that would have the same area would be $$3*25$$ (or $$1*75$$ technically, I guess).
The rectangles you have are $$3*6, 2*3, 3*2, 2*4, 4*2, 10*2$$ and $$9*1$$. The $$9*1$$ needs a $$9*2$$ paired with it to fill those rows and prevent leaving a $$1*x$$ space that cannot be filled. This cannot be done.