A rectangle ABCD is circumscribed around a
rhombus AECF. The long sides of the rectangle coincide with two sides of the rhombus. Also, the rhombus and the rectangle share a common diagonal AC.
B E A
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C F D
What are the smallest dimensions when all the lengths AB, BC, AE, AC and EF are integers?
Find a parameterization of all such integral rectangle/rhombus pairs.
I found AB=32, BC=24, AE=25, AC=40, and EF=30 as a possibility for part 1. However, I have no proof at this point.

Posted by Dennis
on 20080414 15:26:07 