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Four right-angled triangles can be drawn in each of the squares, plus four formed from two adjacent sides of the rectangle - that makes 12.

Then there are two right-angled triangles formed by joining the points UQS and PTR.

This makes a total of 14 triangles.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.