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 A rectangle Around A rhombus (Posted on 2008-04-14)
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.)
 re: How odd! In answer to Charlie: computer solution for part 1 | Comment 12 of 13 |
(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 2008-04-15 10:24:14

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