Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

Age 14 to 16 ShortChallenge Level

Triangle ABC is right-angled at A and side AB is 6 cm long.
An arc of radius $r$ cm is drawn with centre C such that it bisects side AC.
An arc of radius 6 cm is drawn with centre B such that the arcs both meet BC at the same point, as shown below.

Find the value of $r$.

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.