An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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
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?
The diagram shows a polygon ABCDEFG, in which $FG =6$ and $GA=AB=BC=CD=DE=EF$.
Also $BDFG$ is a square.
The area of the whole polygon is exactly twice the area of $BDFG$.
Find the length of the perimeter of the polygon.
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.