11x11 square

Here's a neat trick you can do with an 11 by 11 square...
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative



There's an interesting trick you can do with an $11 \times 11$ square...

It's possible to make five rectangles, each with different widths and lengths, using each of the following dimensions once only: $1, 2, 3, 4, 5, 6, 7, 8, 9, 10$, that can be used to tile the $11 \times 11$ square!

Convince yourself that only one of the arrangements below could satisfy these conditions.

   

Image
11x11 square
        
Image
11x11 square
        
Image
11x11 square


 

Can you find the dimensions of the five rectangles which can tile the $11 \times 11$ square?

Can you find all the possible different solutions?

Here different means not a reflection or rotation of another solution.

With thanks to Don Steward, whose ideas formed the basis of this problem.