Yanqing from Devonport High School for Girls
sent us the only correct solution to this problem. She wrote:
First, I worked out how many types of isosceles triangles there are
that have an area of 9cm ², and can be drawn with integer
I found 3 types:
base = 18, height = 1,
base = 6, height = 3,
base = 2, height = 9.
(These would not work the other way round because it would be
impossible to have integer co-ordinates.)
I then worked out that because there are 3 vertices on a triangle,
and there are 4 directions in which a triangle could go, it would
be possible to have 12 ways of placing one type of triangle around
the point (20,20): you can place it 3 ways upwards, 3 ways to the
left, to the right and down.
I then tried this out and found it to be the case.
Because there are 3 types of isosceles triangles, and 12 ways to
place each one, it is possible to draw 36 isosceles triangles with
integer co-ordinates and one vertex on (20,20) which have an area
of 9cm ².
Well done Yanqing - this is a very clear