Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
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?
There are a variety of ways of proving this. Looking at products
rather than factors may be easier.
The factorisation can be done by inspection using the first and
last terms, as in the second hint.
An opportunity to discuss the representation of consecutive
numbers, consecutive even numbers, odd numbers, numbers that are
divisible by three etc.