wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> medium >> UNEQUAL INTEGERS
        
(Message started by: pcbouhid on Dec 12^th, 2005, 5:47pm)

Title: UNEQUAL INTEGERS
Post by pcbouhid on Dec 12^th, 2005, 5:47pm

Find the minimum area in square meters of a triangle whose sides and altitudes, measured in meters, are six different integers.

Title: Re: UNEQUAL INTEGERS
Post by JocK on Dec 13^th, 2005, 8:14am

Not sure how to do this in a clever way.

I just inspected the set of [hide]primitive integer Heronian scalene triangles of increasing size (up to longest edge 50), and checked for which ones twice the area divided by the edge lengths leads to rationals with small denominators. Multiplying by the greatest common denominator resulted in a minimum area 1050 (a triangle with edges 35, 75, 100, and heights 60, 28, 21)[/hide].

Title: Re: UNEQUAL INTEGERS
Post by pcbouhid on Dec 13^th, 2005, 9:39am

[hide]Right on the spot![/hide]

Title: Re: UNEQUAL INTEGERS
Post by Christine on Jul 4^th, 2013, 11:55am

I found some time ago a question that is part of problem:

what are the dimensions of the most scalene triangle?

What does it mean?