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?
What is the area of the quadrilateral APOQ? Working on the building
blocks will give you some insights that may help you to work it
A pencil AB lying on a table is given a half turn about the end B (so that A moves to A*) and then a half turn about A* (so that B moves to B*). The point C on the pencil is one third of the way from A to B.
What is the ratio of the total distances moved by A and by C?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.