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 Triangulation of Numbers (Posted on 2008-03-18)
```       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?

 See The Solution Submitted by brianjn Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): solution | Comment 5 of 6 |
(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

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