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## 'Uncanny Triangles' printed from http://nrich.maths.org/

Thomas, Jane and Anna were drawing right angled triangles on
squared paper. Their triangles had two sides which were an exact
number of squares long and could not be longer than $15$ squares.
These are Jane's triangles:

They were calculating the areas of the triangles.

"I've got one triangle where the area and the
sum of the lengths of the two shorter sides come to exactly the
same number!" exclaimed Anna, "Look, it's that one!"

Thomas looked at his work. "How uncanny - but so have I! But
look at it. It's quite a different shape from yours."

What were the measurements of the triangles they had drawn?