All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Maximizing product (Posted on 2013-09-19) Difficulty: 3 of 5
In a triangle ABC two items are defined : the side AB=c and the height from point C to this side Hc= k.

What is the maximum value of the product Ha*Hb* Hc ?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 1 of 4
S=Area =c*k/2
As  Hc=c is given, we need to maximize Ha*Hb :
Ha=2*S/a
Hb=2*S/b
Denoting the angle between a and b as Gamma, we have the expression for the triangle area as :
S=a*b*Sin(Gamma)/2
which leads to :
a*b=2*S/Sin(Gamma)
from the above:
Ha*Hb=4*S^2/(a*b)=2*S*Sin(Gamma)
The max. of Ha*Hb is therefore : 2*S=c*k
and the max for Ha*Hb*Hc will be :

                                                    k*c^2



  Posted by Dan Rosen on 2013-09-22 13:36:57
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information