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A rectangle Around A rhombus (Posted on 2008-04-14) Difficulty: 4 of 5
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
+-------+---------------+
|      /               /|
|     /               / |
|    /               /  |
|   /               /   |
|  /               /    |
| /               /     |
|/               /      |
+---------------+-------+
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.

No Solution Yet Submitted by Brian Smith    
Rating: 3.5000 (2 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionDej Mar2008-04-15 10:38:20
re: How odd! In answer to Charlie: computer solution for part 1Charlie2008-04-15 10:24:14
re: Computer aided - solacebrianjn2008-04-15 01:22:10
re: How odd! In answer to Charlie: computer solution for part 1brianjn2008-04-15 00:38:52
QuestionHow odd! In answer to Charlie: computer solution for part 1FrankM2008-04-15 00:30:15
Some ThoughtsWhoopsFrankM2008-04-14 23:16:08
SolutionComputer aided.brianjn2008-04-14 22:24:19
re: computer solution for part 1Charlie2008-04-14 15:53:39
Solutioncomputer solution for part 1Charlie2008-04-14 15:34:31
part 1 ?Dennis2008-04-14 15:26:07
re: Here it isCharlie2008-04-14 14:16:35
SolutionHere it isFrankM2008-04-14 13:40:47
Oh!!!brianjn2008-04-14 11:53:24
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