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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
This problem will need solving in stages by most students.
Perhaps beginning by establishing the required line ratio.
Then by remembering a familiar figure where that particular ratio can be found.
Deciding how that figure can be constructed on the given triangle to locate a useful point.
Finally creating the required line, parallel to the base, across the 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.