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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.

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Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

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Ladder and Cube

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?

Where to Land

Stage: 4 Challenge Level: Challenge Level:1

This printable worksheet may be useful: Where to Land.

Some useful questions:
How long will it take if Chris swims straight to the river bank?
Is the shortest distance the fastest?
What happens if Chris aims for land half way between the previous two points?