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Maximal Rectangle (Posted on 2019-12-30) Difficulty: 3 of 5
Consider a convex quadrilateral whose diagonals have lengths p,q and whose area is A.

What is the maximum area of a rectangle that circumscribes the given quadrilateral?

No Solution Yet Submitted by Danish Ahmed Khan    
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a start | Comment 1 of 4
For the quadrilateral, A = sin(t)*(pq/2)
    where t is the angle between the two diagonals.

If a circumscribing rectangle has a side perpendicular to one of the diagonals, say 'p', then its area is p * (q*sin(t)), which is twice the area of the original quadrilateral.

Also, note that if the circumscribing shape could be a parallelogram instead of a rectangle, and if its sides were all perpendicular to p or q, then that parallelogram's area would also be double the area of the original quadrilateral.

But I haven't proved anything about maximum area.

  Posted by Larry on 2020-01-05 06:49:52
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