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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.

Near 10

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

We requre that $9< \sqrt {n}< 11$, or, equivalently, that $81< n< 121$. 
Hence the possible integer values for n are the $39$ values $n = 82, 83,$ ... $, 119, 120$.

This problem is taken from the UKMT Mathematical Challenges.
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