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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.
At a Glance
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
Contact
A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?
Age 14 to 16
Challenge Level
If the area ratio has to be $1:2$ , what would the line ratio need to be?
What constructions do you know that create such a ratio?
Can you see how to create such a construction on the given triangle?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.