### 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.

# Graph Triangles

##### Age 14 to 16 ShortChallenge Level

This is the graph of the line $y=-2x+12$.

Point P is on this line.

The ratio of the area of the red triangle to the area of the blue triangle is $1:4$.

Find the coordinates of point $\text P$.

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