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.
(In reply to
How odd! In answer to Charlie: computer solution for part 1 by FrankM)
Charlie wrote:
Many results are found. The first few are:
AB = 32, BC = 24, AE = 25, EF =30
Question: doesn't this solution show the same fault as Charlie pointed out in my own contribution, namely that CE <> CF, so that AECF fails to be a rhombus (it is a parallelogram)

Since AB=32 and AE=25, BE=7. As BC = 24, CE is sqrt(7^2 + 24^2) = sqrt(625) = 25, which equals AE, which is the same length as CF.

Posted by Charlie
on 20080415 10:24:14 