W------------------------X
       |                      * |
       |    A              *    |          
       |                O       |
       |             *  * *  B  |	 
       |          *     *  *    |
       |       *        *   *   |
       |    *           *    *  |
       | *      D       *  C  * |
       Z----------------Q-------Y

What is the minimum area of rectangle WXYZ if all lengths are whole numbers, as are the areas of the similar triangles, denoted by A, B, C & D?

(In reply to solution by Charlie)

Charlie wrote: "The guess is that each triangle is similar to a 3,4,5 right triangle....

......  I don't have a proof that this is a minimum, however, so the following program checks for solutions with an area of ......."

I am certain that in preparing this I found an unproven statement which reflected that a 3,4,5 right triangle had the minimum integral area.  My source would have been wikipedia but I couldn't relocate that in a hurry. 

However, the breadth of Maths, and it applications, rests upon certain axioms of which a statement like "The smallest integral area for a right triangle having sides of integral length is a 3,4,5".  We can't prove them, but we know intuitively the truth.

I am impressed that you took time out to bother testing against your given true belief. 

Posted by brianjn on 2008-03-19 08:16:23