Making Rectangles, Making Squares

Lu of St Peter's RC Primary School, sent us the following working:

I use two equilateral triangles and two isosceles triangles to make a basic rectangle.


I have $20$ equilateral triangles and $20$ isosceles triangles, so I can make $10$ basic rectangles.

I can make:

1 row of $10$ basic rectangles long side down ($1$ row of $ 9, 8, 7, 6, 5, 4, 3, 2$ basic rectangles as well).



$2$ rows of $5$ basic rectangles ($2$ rows of $4, 3, 2, 1$ basic rectangles as well).


$1$ row of $10$ basic rectangles ($1$ row of $9, 8, 7, 6, 5, 4, 3, 2$ basic rectangles as well).


$2$ rows of $5$ basic rectangles ($2$ rows of $4, 3, 2, 1$ basic rectangles as well).


$3$ rows of $3$ basic rectangles


Totally I have made $31$ rectangles.