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Making Rectangles, Making Squares

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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
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

$2$ 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).

One row of 10 rectangles oriented shortest side vertical
$2$ 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.