Reply To: Puzzles
@F6EXB_the_frenchy
#112088
(Sorry it took a while to get back to you! I am quite a busy person…)
The triangle is indeed ‘special’ when the median is 4. (As a cheeky bonus bonus question, what if AM=1 instead?)
For the bonus question, Heron’s formula might be needed for the general case, but there is no need for any trigonometry/etc. (There is a very nice, purely geometric solution. See if you can find it!) I therefore FORBID THE USE OF TRIGONOMETRY FOR THE GENERAL CASE! I also deliberately set AM=2 to ensure that Heron’s formula is not needed (you shouldn’t need anything more than the normal area of a triangle formula if you do the reasoning correctly), so I also FORBID THE USE OF HERON’S FORMULA FOR THE BONUS QUESTION!
Good luck.