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

Home > Shapes > Geometry
Minimum Heron Median (Posted on 2009-12-13) Difficulty: 3 of 5
Precisely two of the median lengths of a Heronian triangle are integers. The remaining median length is not an integer.

Determine the minimum possible value of the smaller of the two integer median lengths.

See The Solution Submitted by K Sengupta    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Computer Solution | Comment 2 of 3 |
(In reply to Computer Solution by Justin)

From the Mathworld table given for Heronian triangles with two rational triangle medians we see that the smallest of these has sides {73, 51, 26} and rational medians {35/2, 97/2 (with the third median being 2*SQRT(949))}.

By doubling the size of this triangle there then is a triangle of sides {146, 102, 52} and rational medians, with two integer medians, {35, 97, 4*SQRT(949)}. 

The smaller of the two integer median lengths here is 35.

I have not offered proof that this is the minimum possible value, but it is less than 4550.

 

Edited on December 14, 2009, 1:32 am
  Posted by Dej Mar on 2009-12-14 01:15:54

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 (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information