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.

Rectangle made with two equilateral triangles and two isosceles triangles, with the longest sides of the isosceles triangles forming the longest sides of the rectangle

Rectangle made with two equilateral triangles and two isosceles triangles, with the longest sides of the isosceles triangles forming the longest sides of the 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).

1 horizontal row of rectangles oriented longest side verticle

1 horizontal row of rectangles oriented longest side verticle

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

2 rows of five rectangles oriented longest side vertical

$1$ 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).

2 rows of five rectangles oriented shortest side vertical

$3$ rows of $3$ basic rectangles

3 rows of 3 rectangles

Totally I have made $31$ rectangles.