| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 344.1 | | RAINBO::GRANT | | Fri Oct 11 1985 00:30 | 5 |
| With a quick scan of the 2 digit integers, I'd say it's the triangle with
sides 25, 25, and 30, with altitudes of 16, 16, and 20, and an area of 300.
No proof, since I'm not sure there isn't some skinny triangle with huge sides
and small area that meets the requirements. But I'll bet there isn't.
|
| 344.2 | | METOO::YARBROUGH | | Fri Oct 11 1985 11:38 | 1 |
| Eh? 16*25/2 = 200, not 300. Maybe you mean 24. That works out.
|
| 344.3 | | RAINBO::GRANT | | Mon Oct 14 1985 00:12 | 5 |
| Hmm.. yes: Sides of 25, 25, 30 and altitudes of 24,24 and 20. Those shorter
sides have the longer altitudes.
So, is there one with smaller area? This one has an area of 300, as said
before.
|
| 344.4 | | TOOLS::STAN | | Fri Oct 18 1985 19:42 | 2 |
| But a 15-20-25 right triangle has area of less than that (150),
and its altitudes are integral.
|
| 344.5 | | TOOLS::STAN | | Sat Oct 19 1985 00:45 | 3 |
| I did my own search and found nothing smaller than 150, but, as in the
previously-mentioned search, I can't prove there are no long thin
triangles that I have missed.
|
| 344.6 | | TOOLS::STAN | | Thu Nov 21 1985 01:20 | 4 |
| Peter Gilbert observed that since no altitude can be less than 1,
we need not search any triangle with side larger than 300.
Thus, the search can be limited. I performed this revised search
and found no smaller triangle. Thus, the minimal area is indeed 150.
|