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NZ-NZMO 2024 Problem 3

  • Answer

A rectangular sheet of paper is folded so that one corner lies on top of the corner diagonally opposite. The resulting shape is a pentagon whose area is 20%20\% one-sheet-thick, and 80%80\% two-sheets-thick. Determine the ratio of the two sides of the original sheet of paper.

Dataset text NuminaMath olympiads. Quoted with source.

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BC:CD = \sqrt{7}:3

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