 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  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.) Solution | Comment 1 of 6
`Let i, j, and k be integers with k^2 = i^2 + j^2.`
`The sides of the triangles are`
`  Triangle  k-side  i-side  j-side    Area`
`    XZW     (kk)k   (kk)i   (kk)j     ij(k^4)/2`
`    ZOQ     (jj)k   (jj)i   (jj)j     i(j^5)/2`
`    YXO     (ik)k   (ik)i   (ik)j     (i^3)j(k^2)/2`
`    OYQ     (ij)k   (ij)i   (ij)j     (i^3)(j^3)/2`
`The area of the rectangle is ij(k^4)`
`If (i,j,k) = (3,4,5), we get the minimum area`
`The sides of the triangles are`
`  Triangle  k-side  i-side  j-side    Area`
`    XZW      125      75    100       3750`
`    ZOQ       80      48     64       1536`
`    YXO       75      45     60       1350`
`    OYQ       60      36     48        864`
`The area of the rectangle is 7500.`
` `

 Posted by Bractals on 2008-03-18 10:45:53 Please log in:

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