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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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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?

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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...

Perfectly Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Try a few examples with numbers to convince yourself this works.

You are told that the answer will always be a perfect square - so the factorisation should be easier than you might first think.