The diagram shows a square $PQRS$ and two equilateral triangles $RSU$ and $PST$.

$PQ$ has length $1.$

What is the length of $TU$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.