perplexus.info :: Geometry : Maximizing product

Maximizing product (Posted on 2013-09-19)

In a triangle ABC two items are defined : the side AB=c and the height from point C to this side H_c= k.

What is the maximum value of the product H_a*H_b* H_c ?

No Solution Yet Submitted by Ady TZIDON

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re: solution

| Comment 2 of 4 |

(In reply to solution by Dan Rosen)

Looks right to me when k <= c/2, and I didn't manage to get this far. Nice start!

When k > c/2, however, I think you will find that Gamma = 90 degrees cannot be attained. In this case, I expect that Gamma (and the desired product) is maximized by an isosceles triangle with AB as its base.

Edited on September 23, 2013, 7:54 pm

Posted by Steve Herman on 2013-09-23 09:19:51

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