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'Making Rectangles, Making Squares' printed from https://nrich.maths.org/
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.