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...

Qqq..cubed

Stage: 4 Challenge Level:

The distance between centres of two adjacent faces of a cube is $8$cm. What is the side length of the cube?

I can make an equilateral triangle by cutting off the corner of a cube. If the area of the largest equilateral triangle I can create in this way is $140$cm$^2$, what is the side length of this cube?

A third cube has an edge length of $12$cm. At each vertex, a tetrahedron with three mutually perpendicular edges of length $4$cm is cut away. Can you find the volume and the surface area of the remaining solid?