### 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.

# Traffic Tunnel

##### Age 14 to 16 ShortChallenge Level

A traffic tunnel is being planned. The diagram shows the cross-section of the tunnel. The shape of the tunnel is the same as the graph of $y=\frac49(9-x^2)$.
All distances are in metres.

Which of these vehicles will fit through the tunnel?

a) truck, 2.9 m high, 4 m wide
b) coach, 3.4 m high, 3 m wide
c) lorry, 3.9 m high, 2 m wide

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