perplexus.info :: Geometry : Non existing altitudes

Non existing altitudes (Posted on 2013-10-03)

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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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.

2*S=4a=7b=10c

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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