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
Here it is by FrankM)
For
k = 6, m = 20, n = 15, h = 37, j = 13 for case 1
k = 15, m = 60, n = 52, h = 113, j = 17 for case 2.
that is
AD = BC = 6, BE = 20, EA = 15, AC = 37, EF = 13 for case 1
AD = BC = 15, BE = 60, EA = 52, AC = 113, EF = 17 for case 2.
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.

Posted by Charlie
on 20080414 14:16:35 