1. Obtuse

OK for the mathematicians amongst you <img src=/S/evilgrin.gif border=0 alt=evilgrin width=15 height=15>

Jezza Bear was chatting to Wise Old Olly Owl yesterday discussing the annual event of planting the runner beans. Jezza Bear always creates a "pyramid" of about 6 canes, plants them in a circle and ties them off at the top and then plants the beans at the base. The canes were lying on the floor in a jumbled heap when Olly said:

"OK Jezza, those canes give me an idea that I have been pondering over of late. Can you find the smallest obtuse triangle where the altitude to the obtuse angle and the median to the largest side are all whole numbers. ("smallest" means area BTW)

2. Re: Obtuse

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">No!</span hide>

3. Re: Obtuse

<img src=/S/nope.gif border=0 alt=nope width=15 height=15> 'tis possible sir

4. Re: Obtuse

Perhaps I misunderstand the question because English is not my native language. Isn't the altitude to the obtuse angle the same as the median to the largest side?

5. Re: Obtuse

OK, I see your point.....

1) The median being the mid-point of the longest side

2) The altitude being the height of the said triangle from that midpoint to the obtuse angle

I hope that helps

6. Re: Obtuse

I was being facetious., Jezza

7. Re: Obtuse

Oh...sorry..I thought that was your answer <img src=/S/rofl.gif border=0 alt=rofl width=15 height=15> <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

8. Re: Obtuse

Just to close this one off, the answer is...

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> 5,5,8 where a median and altitude of 3....effectively two 3,4,5 triangles</span hide>

9. Re: Obtuse

Please forgive my obtuseness, but doesn't the triangle below fit the conditions? As far as I can tell, you didn't require that the lengths of the sides adjacent to the obtuse angle should be whole numbers.

10. Re: Obtuse

Ok, looking at the question again it appears that I did not include the fact that they should have been whole numbers.......my mistake. I suppose that if we accept your proposal that they do not have a whole number could we not have a 2, sqrt(2), sqrt(2) triangle <img src=/S/shrug.gif border=0 alt=shrug width=39 height=15>

11. Re: Obtuse

No, that wouldn't be an obtuse triangle - the top angle would be 90 degrees.

12. Re: Obtuse

<img src=/S/note.gif border=0 alt=note width=20 height=20>..to myself Ensure I draw a picture first <img src=/S/blush.gif border=0 alt=blush width=15 height=15>

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