Either Side

A disc with a pencil inside it is rolled around the outside and inside of a wire equilateral triangle. What shape is drawn by the pencil?

Pink and White

The white square slides once around the pink square. Through what distance does the point P on the white square move?

Contact Circles

These four touching circles have another circle hiding amongst them...

3-sided

Age 14 to 16 Short Challenge Level:

Jack's teacher asked him to draw a triangle of area $7\textrm{ cm}^2$.
Two sides are to be of length $6\textrm{ cm}$ and $8\textrm{ cm}$.

How many possibilities are there for the length of the third side of the triangle?

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.