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
Let AB have length 3r. The distance moved by A is then the
circumference of a semicircle radius 3r (3$\pi$r). C moves along a
circle of radius 2r (2$\pi$r), followed by a semicircle of radius r
($\pi$r). The total distance moved by C is therefore also 3$\pi$r.
This problem is taken from the UKMT Mathematical Challenges.