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 re: solution by brianjn)

While it's true that a 3,4,5 right triangle has the smallest area for an integral-sided right triangle, in the solution, the smallest triangle is scaled up 12-fold (in linear measure) to 36, 48, 60.  I'm sure there are other Pythagorean triples, not in the proportion 3:4:5, that would yield lower area.  They just wouldn't fit into the total system presented.

36-48-60 has area 864 while 5-12-13 has area 30.

Posted by Charlie on 2008-03-19 09:22:57