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
re: Here it is by Charlie)
Charlie wrote:
However, BE=20 and BC=6 make EC=sqrt(436), which is not equal to EA=15, and the purported rhombus is not a rhombus but a rhomboid. Likewise with 60 and 20 not resulting in hypotenuse equal to 52.
FrankM responds:
Right you are! Obviously I forgot a constraint. I'll go back and see what a needle, thread, and a plaid patch can do!

Posted by FrankM
on 20080414 23:16:08 