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Two Isosceles

Age 11 to 14 Short
Challenge Level

A quadrilateral has a side of length $1\text{cm}$ and a side of length $4\text{cm}$. It also has a diagonal of length $2\text{cm}$ that divides the quadrilateral into two isosceles triangles. What is the perimeter of the quadrilateral?

If you liked this problem, here is an NRICH task that 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.