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Problem of the Week 839

Weighted Quadrilaterals

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A 3x4 rectangle has sides 3,4,3,4 and diagonals 5,5. Its "weight" is said to be 3+4+3+4+5+5 = 24. Find a quadrilateral with all sides and diagonals having integer length and whose weight is smaller than 24.

Bonus goes to the solution(s) with the smallest weights.

Source: Math Gazette March 1997, p. 18. Article by B. E. Peterson and J. H. Jordan. Result due to H. Harborth and A. Kemnitz.

© Copyright 1997 Stan Wagon. Reproduced with permission.

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2 October 1998