### Golden Thoughts

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 golden ratio.

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?

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# Different Rectangles

##### Stage: 4 Challenge Level:

The most obvious rectangle is that with vertices at $(0,0)$, $(3,0)$, $(3,4)$ and $(0,4)$.

The second has vertices at $(0,0)$, $(4,2)$, $(3,4)$ and $(-1,2)$.