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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: ( Back to comment list | You must be logged in to post comments.)
part 1 ? | Comment 4 of 13 |
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 2008-04-14 15:26:07
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