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...

Weekly Problem 32 - 2014

Stage: 3 and 4 Challenge Level:

Three congruent squares overlap as shown. The areas of the three overlapping sections are $2\;\mathrm{cm}^2$, $5\;\mathrm{cm}^2$ and $8\;\mathrm{cm}^2$ respectively. The total area of the non-overlapping parts of the squares is $117\;\mathrm{cm}^2$.

What is the side length of each square?

This problem is taken from the UKMT Mathematical Challenges.

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