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Non existing altitudes (Posted on 2013-10-03) Difficulty: 2 of 5
Prove that there is no triangle whose altitudes are of length 4, 7, and 10 units.

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution my way | Comment 2 of 4 |
Let a,b,c represent the lengths of the triangle sides in non-increasing order  and S its area.


a should be less than b+c .
S/4 should be less than S/7+S/10.

But 1/4=.25  17/70=.2467

So    -      no such triangle

  Posted by Ady TZIDON on 2013-10-04 07:10:08
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